Interesting question. I first came across this Americanism a few years ago and was confused by it. Here's my question: https://www.italki.com/question/375582 In the intervening years, using 'reaching out' as a synonym for 'contacting' has - needless to say - become more common in the UK. Like James, I'd also find it 'cringeworthy' to use it in a British context.

Perhaps I should add that, probably, you'd only use "thank you for reaching out" in response to a first contact from someone, or in response to someone approaching you with a new topic or thread. https://ell.stackexchange.com/questions/154792/thanks-for-reaching-out

"Thank you for your message" is a little more formal in my opinion, good for a business context. "Thank you for reaching out" may be more applicable to an email from a friend or a social context.

YOUR message ofc

Yes. By the way, there's a tiny, unimportant typo in your post I think. I imagine you intended to write "Thank you for your message".