Migrate browser extension to Manifest V3

[taras-yemets]

Starting in January 2023 in Chrome 112, Chrome may run experiments to turn off support for Manifest V2 extensions in Canary, Dev, and Beta channels.
Starting in June 2023 in Chrome 115, Chrome may run experiments to turn off support for Manifest V2 extensions in all channels, including stable channel.
More details on the transition to Manifest V3

/cc @muratsu @jjinnii @ryankscott

[vdavid]

My comment from Slack: "It sounds like a bunch of alterations will have to be made to Manifest V3, and the timeline is pretty relaxed, so I suggest we wait a few months until there’s a wider adoption of the new format and perhaps a V3.1."
(after @philipp-spiess's link: "I have recently stumbled over this repo and have read the hilarious readme")
So I'd de-prioritize this

[texastoland]

It seems imminent now: