Yeah you want the titanium networks projects, which are essentially a bunch of web proxies exactly like what you ask for.

I used to use Metallic, but it's not actually that good and not maintained anymore.

Here is a public instance of holy unblocker: https://uc.robby.blue/scramjet

This is one of their flagship projects, and is what you want. Self hostable of course, code on github. I preferred the projects that give you internal tabs though, like hypertabs or anura.

Public anura instance: https://anura.pro/ (but anura looks like a pain to self host, it's much more complex)