I went down that rabbit hole once and it’s really hard to find a foss app that is enjoyable to use and actively maintained. Condution (https://www.condution.com/) seems to be one of them but I never tried it as it looks a bit too much for what I personally need.

Not open source but e2e encrypted and privacy focused is lunatask (https://lunatask.app/). They have a free plan and you can get access to the iOS beta (the app is fully functional). I don’t used it anymore but I paid for Lunatask and it helped a lot making order in my brain and switching from bloated apps to a more minimal todo approach. It’s highly opinionated, but it implements more than one “method”.

Currently I’m using https://github.com/sodenn/2do-txt because I switched to the todo.txt method, which better fits my need for a more minimal approach to those things. The app has ios/macOS version (with tauri build replacing electron) and you can sync with whatever you want (i use syncthing).

Hope it helps, the todo landscape on ios is a nightmare.

Ente Auth seems open source: https://github.com/ente-io/auth

But the need for account is trowing me off a little bit. I’ll give a try to 2FAS as well.