I've documented my approach which is to not use an app at all, but instead a single text file that becomes a list of things done by the end of the day: https://jeffhuang.com/productivity_text_file/

The notes you take during the day, and past lists are all easily searchable in a text file.

I think https://momentum.earth/ gets a few things right (no affiliation)

Check out Amazing Marvin (https://amazingmarvin.com/)

I build something that for me addresses 1-3 (7 I guess depends on how you use it). Feel free to check it out: https://thisweek.rocks/

(localization for weekday names coming after my vacation)