As a quick followup here, I was able to easily put the same exact public key onto Github.com and ssh authentication went through without a hitch using exactly the same key pair. I did also try standard RSA key pairs on esoui as well, so the issue does not appear to be protocol specific.
I think it's reasonably safe to say I'm not incorrect with my process here and my setup isn't critically broken on my end, but it appears that git support on esoui is broken in some way from the server side. Maybe it's not worth fixing, but it is still disappointing.
Maybe the setup instructions for git should be updated to reflect that the option is non-functional, unless I'm the only one having issues (or even trying to use the services).
Thank you, wookie for trying to help. The extra debugging info was interesting, but not helpful. A connection attempt to github shows what should happen when offering a valid key.
Code:
...
debug1: Offering public key: /c/Users/<username>/.ssh/id_ed25519 ED25519 SHA256:TRo1+EbUEgApsrOXXMMbOTmMMkcRD/0rOuQBC9x84sU explicit
debug1: Server accepts key: /c/Users/<username>/.ssh/id_ed25519 ED25519 SHA256:TRo1+EbUEgApsrOXXMMbOTmMMkcRD/0rOuQBC9x84sU explicit
...
But obviously I'm not getting that response from esoui, so probably my public keys are being "missed" or ignored by the server in some way, and I don't have a way to reasonably fix that issue on my end.