Who would you write like this to?

[Rolf38]

'You won't feel like this forever. Promise!'

Does this sound quite informal?

I'd say informal, familiar. (But not suspiciously so, if that's where this is headed). So anyone from a friend/sibling/partner to possibly a close colleague.
Depends on the context, I'm afraid.

Informal. Someone you have a relationship of some sort with, either family, close friend or partner.

At work we’re being encouraged to write Better Letters i.e. concise, friendly, informal & don’t worry about grammar. So even the tax office may send you something like this.
Give us a clue.

Pretty much anyone depending on the circumstances. If it was a stranger with a wrong number who texted to say they were feeling down, I can imagine replying with that (and 'this is the wrong number btw').

I'd say its from someone who's been there and showing empathy in a non creepy or over familiar way

Just tell us why you asked.

Depends on context, doesn't it? What conversation comes before? Have expectations been dashed, is the receiver tired of waiting for something? And the sender promising - it's in their control perhaps things will change , or they know for certain it will be fine someday or not and they are just saying that to appease them. But tricky really. Why? Did you get it and think it's for someone else?

This is like vaguebook'ing for Mumsnet.

I don't understand; what's your AIBU?

If it's, AIBU to ask a random question with no context, the answer is yes.

Trump?

It could be anything. I could be a response to someone saying they don’t understand how to do a part of their job, someone who has a cold, someone who votes Tory.

Need context but it's pretty familiar, a close friend I think.

It was someone who was trying to encourage me believe that I wouldn't feel the way I currently am permantly.

I was questioning the tone and formality.

I Recieved something similar today:

'Let me know if you want to make any changes (I won't be offended promise)

Does this have a similar tone? It seems really informal - the use of 'promise' rather than 'I promise', or even just using the word 'promise' all together - who would use the word 'promise' in contact and why?

It sounds friendly

But better if you just say who it was from so people can comment if it’s an appropriate tone from that person

'I won't be offended, promise' sounds jocular to me.

Informal, unprofessional and irritating.

Are you unhappy with the tone and wanting to raise a complaint?

someone trying to help you. it could be someone in a formal-ish position who has drafted a letter for you, but feels that a friendly tone is what you need in order to encourage you to take steps which will help you move on with something that you need to get through/ over/ past. (A less formal approach to make you comfortable with the idea of a 'stranger' helping you, if you might be uncomfortable with that - to promote a sense that you don't need to be afraid of this person's reaction)

otherwise a friend or family member who is worried about you for some reason.

🤦🏻‍♀️. OP Can you give any more info or context?

Is it from a social worker?

Are you normally so suspicious over nothing? Honestly, without more information this is a question no-one can answer.
How old are you?
How old is the other person?
What was it about?
Was it a work / home / friend situation?
Why does it matter?

the 'promise' would grate on me if it was in a professional context, but there are some folk out there who would see it as being open and friendly, not weird

Yes, this. I would probably only write this to someone I'd given birth to or was otherwise very close to.

'promise' to some people would just mean 'you can rely on me'.

but without knowing the context, it's all meaningless. do you have ASD? my son fixates on word choice. sometimes he struggles to understand that it can mean different things in different contexts. so I'll be randomly guessing, and eventually he will tell me the context and I will have been completely wrong, and there is an obvious meaning that I just didn't get, because the context was missing. So then I have to start again...