@dirtychinchilla it sounds like you're similar age/ experience to me, I graduated 6 years ago and now a chartered engineer. It sounds like you're frustrated/underpaid and not enjoying the role. I have to say I've got no idea what a product manager is though! I work in construction/consultancy.
It sounds like you have a lot of responsibility for a package ~£50k or just under. I've just got a new job shy of that figure. I wanted more but tbh I was keen to leave and I think my marketplace is slightly deflated due to covid. You do know that for the bracket under £50k you pay 20%+12% NI and for >50k it's 40% +2% NI i.e. 10% extra/not as big a difference as you may believe. If you earned 55k, you could also salary sacrifice £5k to your pension then pay no tax in the upper bracket.
For your new role I'd always say inflate your salary that you want (dont just go for the same +£x K, add on the costs of the extra mileage, the risk amount etc)
I wouldnt take a counter offer unless they offer you more money/resolve your current issues. I think employers just count on people not wanting to move on due to "risk"/uncertainy etc.
For me in 6 years postgraduation I've lasted:
1st role - 18 months (moved due to location)
2nd role - 2.5 years (moved due to lack of work/projects)
3rd role - 2.5 years (various reasons but salary and them furloughing staff was one)
4th role - start imminently.
In every role thus far I've been glad I've moved and always received the highest salary jumps when moving. My imminent house move also aligns with new job!
re: moving house, if you speak to a broker some lenders will be OK with offering you a mortgage in your probation (if the role is similar, no massive inflation to earnings and you can demonstrate all your previous career earnings with no break). I'd want a good salary for working in the south west but thats just me!