I am confused as to why a faulty battery would cause crashing
I was in the same boat. My battery didn't appear bloated at all and the crashing wouldn't always occur, just sometimes, and usually when the phone was around (or less than) 40%. I tried turning off background tasks, resetting the phone, installing an insider ring, etc., but in the end I gave it a go and it did seem to be the battery (Note, not all replacement batteries are created equal, I got a dud that was even worse than the original battery). After replacing it I went from about 3-5 crashes a week to going on 4 weeks with no issue.
I agree, it's really strange but after being skeptical I do think it was the battery. Most of my crashes happened when I got an incoming text or unlocked the phone (on a low battery level) so I think the issue was the phone tried to pull too much power from a weak battery and just crashed.