mailbox.org has been pretty good. you can also sync contacts and calendar using DAVx5 on android. They don't have any official apps. but thunderbird mobile works well.
For many years it was just that I didn't trust anyone not to hand my data over to someone else, whether that be governments, companies, or (unintentionally) hackers.
Nowadays I would probably trust Proton Mail, since they have pretty good encryption. But as you point out then I would be dependent on a provider.
Currently I mostly have problems when I lose power or when my ISP renumbers. Probably I should just migrate and save myself pain from Google and Microsoft making it hard to send mail to their users (which is most people on the planet).
Oh shit, yes, hosting at-home and with a non-static IP sounds like hard mode, oof.
I am hosting at a server provider (guess I am dependent on them, but at least it's on their existence, not on a policy-of-the-day), with a static IP. Had no problems with MS/Google, only with T-online, who wanted me to host a website on the domain with clear contact information.
I'm using Hetzner in Germany. Need to message them to say you want the relevant ports opened (spam protection measures), happens within an hour usually.
I quite like their service, but of course use full disk encryption etc