Having a way to automatically use an archived version would be lit though

Or at least to automatically make the archive!

A few years ago I tried to use ArchiveBox for this purpose, but it had problems, and development didn't happen much since then.

Then recently I have found Linkwarden. That also seems to be a tackled together solution, like the installation instructions and not just unclear but also incorrect, and the real steps are weird...
Bit it seems to work so far. It can't handle multiple versions of a website nicely, but at least you can submit the same site multiple times, with some minimum time limit.
Haven't figured out yet how to easily forward links to it from my phone, though.