To feel uncomfortable with this man?

I think @MmedeGouge has summed it up perfectly. You were being kind offering the hand of friendship but he's obviously taken it as meaning something totally different. This is where you have to be so very careful, don't offer to go for coffee with men you hardly know, especially men who have disclosed mental health problems to you and definitely don't give them your phone number, why did he even need it? Unfortunately, he's obviously taken that as encouragement. Sadly, you are leaving yourself wide open to this kind of behaviour. I am not criticising you in any way, you sound like a lovely caring person, it's other people who can misinterpret your actions. When my sister was younger, she had a Saturday job in a little gift shop. Every week a man used to call in, buy small items and eventually started to chat to her. He disclosed he had severe depression and mental health issues and she felt sorry for him as he seemed very lonely. He was a lot older than her and she never imagined he was viewing her friendliness in another way. It got to the stage where she'd make him a coffee and have a chat (it was a very relaxed "Hippy Boho" type shop). However, one day, when the shop was empty, he came behind the counter and attacked her, he said later that he thought she'd fancied him as she was so friendly. You have to distance yourself from this man, keep it to a brief hello if you see him, don't stop and chat and block him on your phone, the fact that he's messaging you so late at night is very worrying.

He fancies you OP. He doesn’t care that you’re married and probably hoped you didn’t care either. Sounds like he has stopped texting you now though so maybe he has got the hint.

I agree, it all seems to be considered your fault/responsibility.
And even if he is acting in all innocence, for whatever reasons of health/circumstances, it's still not your job by default to manage the whole thing.

I didn't say I thought people had to be perfect Nor did I suggest he was doing anything approaching criminal.

I'll say it again: I think he probably fancies her, but I'm open to the possibility that he doesn't. I will say that for me, from life experience, this sort of behaviour often means a man fancies you. Others on here are saying the same from their ow experience. Either way, there are issues here with boundaries and yes, with socialising/social etiquette.
The OP offered 'friendship' in the sense of a sympathetic ear and some casual company. Not the kind of friendship where he messages her about fairly inconsequential things with frequency and at unsociable hours (and yes I realise that as a carer, or just out of his own personal preference and habit, he might be OK with messaging at those times; but most people realise that they are generally considered unsociable hours).

You seem very keen to criticise the OP for this situation, and are very keen on her taking full responsibility for his feelings (withdrawing gently), but it takes two; this man, whether innocently or not, is causing a situation where she may have to back off a bit, or completely withdraw her offer of a bit of sympathetic company.

You intended a casual acquaintance with this man. Unfortunately he misunderstood your intentions. He really should not have but he did.
Some men cannot view friendship with women in a platonic way.
I guess he was testing your boundaries by inviting you into his house and texting you late at night.
If I were you I would avoid any further contact with him.
In future if someone starts to share very personal information with you at a very early stage in your acquaintance do take care. They made need a lot more than you are prepared to offer. I have only learned this by experience and like you have had my fingers burned on occasion.
However all that being said you sound like you have a kind heart and are very well intentioned. Do not let the negative comments on here upset you. What you intended originally was very well meant. It’s unfortunate the man either accidentally or wilfully misinterpreted them.

Not everyone is perfect, someone who's isolated with caring responsibilities is likely a little rusty with socialising. I think OP has made many assumptions which are likely untrue. Asking someone in for coffee, and accepting when they decline, is hardly a crime and certainly doesn't mean they fancy her! He knows she has a husband.

She offered friendship and has realised she doesn't want it with this man. That's fine, but I hope she withdraws gently.

Lots of men see ordinary friendliness as a come on. I wouldn't bother spending any more time with him.

He was trying it on inviting her in for coffee when they'd agreed a cafe. And sister present or not, being in someone's house is not the same as being out.

I said he 'probably' fancies her, but I'm open to the possibility that he doesn't. Yes, I agree, he lacks a feeling for social etiquette. But texting with such solicitude about something they could have talked about casually when they next bumped into each other is not just about etiquette; it's a lack of awareness of boundaries and the extent and nature of their relationship.

She may well have said cafe, but he probably didn't think anything of asking her in for a coffee, and it isn't like he was alone, his sister was present too 🤨🤨

She said no, he accepted it. No harm done.

There's no indication he fancies her at all. More that he lacks social etiquette with the texting at all hours.

Whatever coffee he prefers, the OP's already said she specified a cafe
She didn't 'ask him for coffee and a chat', she offered it if he wanted to, as a bit of friendly support.

I think he is lonely and probably fancies you, OP, and has poor boundaries/judgement partially because of this. And I'd feel weird about it even if he were a woman, TBH (I have had a similar thing with a woman, who didn't fancy me but was clearly lonely and needy).

I don't think you need to avoid walking the dog or change routes or anything. If you want to, I think you could still say yes to the occasional coffee and chat out in public if he asks, and be friendly when you see him, but be firm in staying a little bit removed.

Did he pay for the coffees you had? You mentioned he said you could pay for the coffees next time. I think you should have each bought your own but if he paid I'd say he's trying to keep things platonic by saying you can take turns paying going forward..

nope, that’s classic “pin down the next date” behaviour!

The fact that you’re married means nothing, plenty of people have affairs, sadly, so he won’t necessarily be thinking it’s purely platonic just because he knows you’re married.

IME a certain type of man would only talk to you, help you, hold the door for you etc if they fancy you. Women they don’t find attractive are literally invisible to them. If someone pays them attention or gives them the slightest bit of attention they can only interpret it as being because the woman fancies them. They can’t imagine a world in which you pay them any attention or help them in any way unless you want to shag them.

I’d wager that this is what’s happened here. He’s taken your gesture of kindness as a come on.

You mentioned that he’s a coffee snob - it might just be that he doesn’t want to spend £3 on a shit coffee if he has good stuff at home. But equally the rest of it does just sound like he’s got a crush and is happy to have the flutters of a new burgeoning relationship (in his mind) to distract from his break up.
Lesson learned, being kind to men is not the same as being kind to women.

Note to add: not all men etc

He isn’t your problem, your own boundaries are your problem.

Any gut feeling needs to be listened to. It’s a shame he is lonely, what’s happening would not be great if it was a woman either but there is the added issue he is a male.

I'd feel a bit cornered as well.

No good deeds go unpunished.. He made you feel uncomfortable- listen to your gut instinct. He is pushing your boundaries.

Oh dear. I have a friend like this, she's very empathetic and smiley, and all sorts of waifs and strays are attracted to her. It starts off with 'oh she's lonely so I said let's go for a bike ride' then it ends with 'omg I'm so drained by this person and now they want me to go on a day trip to East Kilbride but I'm sooo busy'.

Rinse and repeat, year after year. It's tough because you don't want to turn your back on a needy person but the problem is... they're needy.

It seems clear that he has misinterpreted your intentions. Asking him for coffee was probably a big thing for him bearing in mind his personal circumstances. You need to pull back and draw new boundaries.

I think he's lonely and probably lacking in social skills a bit.

You were meeting for coffee and a chat. That's exactly what he offered. I wouldn't read anything in to offering coffee at his home.

Did he pay for the coffees you had? You mentioned he said you could pay for the coffees next time. I think you should have each bought your own but if he paid I'd say he's trying to keep things platonic by saying you can take turns paying going forward.

Does he work? Being a carer is pretty lonely at times. Being up at 1am when you care for someone with health issues is sadly pretty normal in a lot if cases. It's also a pretty lonely time to be wide awake.

It's upto you what you do but I don't see that he's done anything wrong other than grabbed at a friendship opportunity quite keenly. There's no reason not to keep chatting to him or going for coffee now and then. Just make sure you're not always available so that it stays as an occasional thing not a weekly event, if you don't want it to become a routine.

This

I don’t think he is creepy (just read your first message) he’s just lonely. He probably feels that as you’re married that you’re safe to be friends with as his intentions won’t be misconstrued. Poor guy. You’re totally ok to let him know your boundaries in the friendship

It doesn't really matter that he might be lonely etc, he's overstepped a boundary. What matters is that you feel uncomfortable. Listen to that and act accordingly.

Because YOU reached out a hand of friendship with a random stranger. Recognising someone from dog walking does not make a friend.

He prefers the coffee he makes so asked you in, that's not weird, he probably didn't think anything of it.

If you don't want him to be a friend, that's absolutely fine, but then don't start asking him for coffee and a chat. You're sending mixed messages. Just go back to a polite wave and think more carefully before offering friendship again.