If your instance has custom emojis defined, this is exploitable everywhere Markdown is available. It is NOT restricted to admins, but can be used to steal an admin's JWT, which then lets the attacker get into that admin's account which can then spread the exploit further by putting it somewhere where it's rendered on every single page and then deface the site.
If your instance doesn't have any custom emojis, you are safe, the exploit requires custom emojis to trigger the bad code branch.
I'm not particularly familiar with XSS but I'm curious how a frontend exploit can compromise an instance?
Presumably the injected XSS stores the admin's JWT somewhere for the exploiter?
Then using that JWT they can effectively login as the admin which gives them access to whatever admin dashboard there is, but does that actually compromise the backend at all?
Front-end parses the emoji incorrectly allowing JavaScript to be injected.
JavaScript loads for everyone to views a page with the comment and sends their token and account type to the hackers domain.
Hacker parses received tokens for admins and uses that to inject redirects into the front page of the Lemmy instance.
To answer your other questions:
IMO there probably should be better parsing to remove this stuff from the back-end, so I'm not sure the front-end solution is the complete solution, but it should get things largely under control.
Back-end is theoretically not compromised besides needing to purge all the rogue comments. Attacker presumably never had access to the server itself.
Probably needs to be a mass reset of ALL passwords since lots of people's tokens were sent during the attack, so their accounts could be compromised.