I have searched for a way to do this and never found a good answer, though there have been tickets created in the past (#142818 & #405549).
Apparently, the chromium devs never created a chrome://flags override for "broken" SSL with password saving. This would seem to be the easiest way to fix this annoying "feature" (via flags). I DO understand completely why they block it by default.
Since there is no override to my knowledge, I had assumed that you would need to import the given self-signed certificate to a trusted root area in (Windows) store. This does not appear to work either.
Has anyone been able to get this to work? I can live with the warning - just not the lack of password saving. I spend most of my workday in a dev environment and need to keep re-entering passwords dozens of times a day (copy/paste).
EDIT (20 Feb 2023)
Please note Firefox DOES save and offer a password once you get past the warning/exempt site page. This Question is strictly in regards to Chrome. There is still no way to allow this similar to Firefox as far as I know (via flags or an exempt sites 'list').