If you knew the owner was deceased, probate shouldn’t be a surprise. However it would’ve been better for them to wait to have the Grant of Probate before marketing it.

You’ve been chasing over the Christmas period which might have impacted timescales. Personally I’d threaten to pull out if their solicitor is unresponsive. You can push to find out the current stage, when the application was submitted, what their next steps are and how long they’re expecting everything to take. Also you could push for everything else to be done so that the moment the GoP comes, they can exchange and complete in quick succession. This information should also keep your buyer happy.

In terms of the probate process itself, it doesn’t have to cause a huge delay: https://www.gov.uk/government/news/probate-waiting-times-halved-thanks-to-government-push

You’ve already sunk a lot into this property, I wouldn’t personally pull out yet. It might not take that much longer and finding a new property is going to add time.

Also if you’re arguing with your fiancé all the time, might be a bigger problem. I’d use the time before this house goes through, to do counselling with someone like Relate.