I am using i3 but what bugs me is that tabs now seem to be part of the browsers.

There's no elegant way of telling Firefox to never use tabs, always open a new window. There are some extensions pretending to this, but the experience is terrible. There actually is a new tab created which is then detached.

I don't usually use Chrome, so I looked up wether it handled this, but it seems to rely on extensions too.

Qutebrowser works, but it has other limitations, such as poor extension support.