I like your style. I went looking and found “switchbar” which kinda/sorta eases this bouncing between browsers idea:

…google.com/…/klgpknafjlhnpkppfbihchgfebbdcomd

It’s not elegant, but it supports the workflow you suggest. I kind of like the idea of using Edge for google.com and Chrome for microsoft.com. I’m not optimizing my experience (it may in fact be very sub-optimal), but I’m also using competition to neutralize potential shenanigans.