Cat with heart condition - indoor kitty or not?

[Sadandconfusednamechanger]

Our cat has only been with us about a month. He was a rescue cat and is approximately 1 year old. His previous owners gave him up because there were too many pets.
A couple of weeks after we got him, he had a day when he didn't eat. He then had very laboured breathing. He was taken to hospital and admitted and put on oxygen. The vet asked about poisons, trauma etc. He hadn't even been out yet.
It turns out he'd suffered heart failure due to a heart condition he was probably born with. They didn't even think he'd make it but he's back home and responding very well to medication.
The first vet who specialised in cardiology was thinking that he could maybe go outside if he recovered well. The get we saw for his check up, at the local vets, said no she would definitely advise against it in case he didn't come back for his medication (morning and evening ones taken with meals).
Does anyone have any experience with this? He does not have a long life ahead of him so I think the first vet was thinking the risk of him being late back was there but it was a balance with his quality of life and ability to lead a normal life. I am not sure.

Poor wee lad - at least he's found his home, though.

Do you have a reasonable space for him to be in and company for him? (I think there's a lot of difference between having an indoor cat in a small space who rarely sees people to a cat in a large house with a more constant presence from his people.)

We don't have a big house but he has the run of it. I am home a lot so he has me around plus the kids after school.

Now to complicate things, this week he did his business in the hallway ( no 1 on Tuesday night, number 2 on Wednesday morning) then he urinated all over the sofa this morning and pooed on the kitchen floor beside his litter tray (which for the first two weeks he was using with no problems). I have changed his litter back to catsan non clumping as I changed to clumping the day before he went into hospital. Any other ideas why the change? And how best to get rid of the smell?

Bumping to just ask if anybody else out there has had a cat with a condition needing medication, if they could tell me whether they were an indoor only cat or if they allowed them outdoors?

(Please)

I'd be keeping him in for at least the time being because that timing of medication is a fair point that the vet made - when you let them outside (unless you have a run or something) you're pretty well throwing him to the wind because he'll come back when it suits. It may suit him to have a routine but there's no guarantee.

The peeing and pooing out of his tray is a complication though. How is he generally with being inside and how has he reacted to the reversion to his old type of litter?

Keep him in for the time being- see how his meds stabilise him.

Thanks SecretNutellaFix and cozietoesie
When he was first home he seemed a bit weak and shaky on his feet - understandable I guess when he had been through all that he had. However, nce he'd been back a couple of days he perked up a treat, his appetite is back with a vengeance (when we got him it would take him all day to eat his breakfast and all night to eat his dinner, but now he wolfs it down within 5 minutes, plus he's waking me up early to ask to be fed. So I definitely think he is feeling much happier. He is trying to get out when we open the doors too.
On the other hand, we don't yet have a cat flap (would be silly to fit oe if tere's any chance of him being an indoor cat?) and he is only a week into being home from hospital, so he definitely won't be going out for the time being .

PS He is tons better using his litter tray now I have changed back from World's Best to the non-clumping stuff we started with. I think he didn't like World's Best - which is odd because it gets such good reviews, but I suppose he can't read and has his own mind! .
Feeling very sad for him, a young cat, that he has such a crummy prognosis .

Sorry for typos...