People forgot what it was to Google back in the day, where google was always showing a notification box to download their Google Chrome. So MS now uses their tactics. But they have grater leverage - they control OS and browser. And in this way they are not shooting themselves in the foot, but trying to keep the casual user base who doesn't care what color their internet gatway is.
The only pity would be Windows not respecting default browser choice when opening links.
And talking about Manifest V3 is some kind of mistake from MS... well, it is a chromium browser, what would you expect? Guess MS doesn't want to fork too deep from chromium. If users care about Manifest V3 then MS greatest competitor - Google - is also out of equation.