My goal is to have a very secure, easily maintainable router. Should I simply buy a router that auto-updates its firmware? If so, which one? Do manufacturers provide auto-updates?
Does OpenWrt provide a system for auto-updates? From what I've read it appears that it does not. It also appears that updating OpenWrt is a bit of a pain, although I'm not sure. I'd be willing to spend 10 minutes a couple times a year to ensure that my router's firmware is up-to-date. Is this doable with OpenWrt? If so, is there documentation that shows what must be done?
The RPi4 has a ton of cpu power and operates on a micro sd card. Buy two sd cards and when time comes to upgrade write the new sd card from your PC, transfer settings and then swap the cards. Easy.
There is a paradox in your question. It is more secure to update your router yourself. There are things that can be done to make the update process quick and easy.