OP I'm not a doctor and I might get flamed for saying this
I am going to stick my neck out and say I'm surprised by your experience
You're 40, right? Your bloods came in normal for meno - yet they still decided to treat you with HRT rather than treat the thyroid, which will link to your heart issues, and it's taken a month to send you for an ECG? I read your thread wondering why you were being given HRT tbh. Hair loss and palpitations and sub optimal thyroid results - why was that not their priority?
I had a nervous breakdown in July and I'm recovering well but had to do a lot of research and tests because I wasn't sure the doctor was right about the physical impact of it, which seems to be lingering. I now think he was right - it is all due to the breakdown which was a long time coming - but all bar one friend has said to me "is it peri". I'm 47 and that seems to be the default assumption. The one friend who agreed that the physical impact of a nervous breakdown may be long, and it's not going to be peri, is...a GP friend!
I mean this kindly, but did you jump to peri, and did you ask the doctor to treat that first? It seems very poor form to go for HRT as priority when the patient has sub clinical thyroid and reports palpitations.
Btw you mention climbing Snowdon. That's amazing, I could never do that. But if you're at sub clinical thyroid and have heart issues at the moment, I'd be careful in terms of activity.
The flutter you mention sounds like atrial flutter, I've had it a couple of times, my mum has full blown atrial fibrillation since her 70s. It is scary, I know.
I hope you get treated correctly but I'd really focus on thyroid and heart, and ask yourself why you wanted HRT. Sorry but it feels to me that the world is currently obsessed with peri and meno. I have been in treatment for depression and anxiety for decades but still get concerned parties saying "is it peri". everything isn't peri!