Tootfinder

and so, once again, the 'solution' isn't in the distro or legacy, it is in the wiki on the internals of Evolution where I just incidentally learn it can be a flatpak or not, and thus there are TWO .local/share folders to wipe. So I delete all accts in Evo, empty trash just in case, exit, wipe those folders, go into Settings, delete the Google connection which shows as two identical so delete them both, reboot.
On boot, go straight to settings which shows none, add Google and I'm in, quick as a wink. I start #Evolution, and lo, there it is, my account fetching emails!
Now to figure that #mastodonel thing and why mastodon.plstore is so problematic.

Found an obscure hint that perhaps instead of authenticating through #Evolution I should instead authenticate through the #Gnome settings for attached accounts, so I tried that approach, this time it asks for far more permissions (8 in all) but, you guessed it, a classic Sam Beckett "No Answer" and the terse response, "timed out".
So the app doesn't matter. The browser doesn't matter. The account or any legacy cruft doesn't matter.
Does this leave as the only explanation that perhaps Google no longer provides OAuth2 tokens? Surely that would be all over the news if true, but I'm running out of local culprits. Also Emacs inability to authenticate Mastodon suggests its neither google nor Debian per se? Maybe I should spend my time more productively slamming a car door on my fingers?
I have a dread feeling wiping the laptop and carefully reinstalling from scratch will not work.