This doesn't address all the issues you raise, but my hack to deal with the Twitter sidebar is to set it to a language and region I don't understand.

1. Click "Show more" at the bottom of "What's happening"

2. Click the "settings cog" at the top of the page

3. Uncheck "Show content in this location"

4. Click "Explore locations" and choose a location whose language you can't read and you know nothing about.

And to avoid outrage leaking to me via people who end up in my main feed I simply aggressively mute pretty much anyone who talks about politics or similar. Sure, I therefore lack their signal but avoiding their noise more than makes up for that.