I love a charming and characterful cottage as much as the next person - and, indeed, I live in one, of sorts, and from that perspective I would say don't underestimate how much of a money pit they usually are. Something will always need fixing. And something made of three cottages bolted together may well have peculiarities - mine has a bit of this going on and has rather a lot of different sections of roof to contend with, not to mention quite an awkward layout (needing to go through rooms to get to other rooms).
I can live with all that partly because I just love old houses and that's the deal, and also because my house was cheap! What you are looking at is not. Which is not to say don't buy it, but be really sure your budget can absorb the likely costs in terms of maintenance - and heating; you mentioned part of the house being colder? Where you are now is warm, how are you with a cooler house?
I asked the things I asked because I was wondering whether you might be after an aspirational 'forever home' type thing that's perhaps slightly beyond your reach right now in the area you're in. From your response it does sound a bit like that might be the case, plus there's a combo of everyone feeling a bit stuck and mopey for different reasons, plus-plus you're actually pretty comfortable where you are so there's no great impetus to move on. But in your initial post, even in that quite comfy mates rates situation, you sound quite burned out by work and overwhelmed by the idea of having to keep going at the same pace. So I guess my advice would be maybe listen to yourself about that.
If I were you, I would probably be looking for something more affordable. And maybe it wouldn't be detached and have a roof snug and all that jazz, but it would be less pressure on yourself. I bet if you compromised a bit, you'd find something that ticks many, many boxes - and would move you on from your current status quo. It might not be your forever home, but to be honest I don't really think those exist anyway. I think maybe you've been looking for so long, all the while feeling a bit despondent about things that have played out in a way you perceived as negative, that nothing really feels perfect - so embrace that, and look for something nice.