The ever shrinking tab sizes in Chrome/Edge as you open new tabs is a really bad UX. One reason I often keep too many tabs open is because I can't read the title to decide which of them I could close. The tab bar becomes difficult to use as it grows, and compounding the problem, less likely that I'm able to shrink it, as I can't read the titles.
Vertical tabs, placed on the left or the right side of the window, next to the content, solves this issue. It also allows for more vertical space to be dedicated to the web site. Vertical screen real estate is at a premium, for example, on a typical Windows laptop with a 16:9 screen and the massive task bar on the bottom. The tradeoff is that pages will be in a smaller space horizontally, however, given that most web pages scroll vertically and use extra horizontal space poorly or not at all, and are responsive nowadays anyway, this would still definitely be a huge net benefit in my opinion.
I'll be forever using Edge if this feature is implemented, and implemented well, cross-platform (not through some sort of hacky browser extension or Electron/Vivaldi-like "solution"). I'm sure many people would agree.
@sambul95 Tab Groups only partially solve one of the problems mentioned by the OP. They don't solve the real estate issue and I'd argue they're only a partial solution to the UX issue. Vertical tabs are a game changer and Edge needs them.