Create a permanent redirect to any other site should transfer any search "scores" onto the new site. You can also request google to de-list the ___domain from search, which should reset any value that the ___domain has acquired from the time you owned it.

If the account is validated on large platforms, it should be a good idea to remove those from the account as a way to signal the platform that it is no longer validated on that site.

Some TLDs/registrars let you park registrations. They won't appear in the DNS, but they can't be registered by anyone else. Or there is a delegation to some internal hosting service that the registrar operates that is an empty zone (i.e. no A, MX, etc.) so there is nothing reachable.

I've done this with zones I've had for a while - it sucks since you want to be a good net citizen and not let the zones be used for spam/attacks. You end up paying for a ___domain for years after you stopped needing it.

Delete any accounts you've created using that ___domain, those could be taken over by the new owner. Especially important if you ever used email on the ___domain.

Once you let your ___domain expire you no longer have any say over what happens with the ___domain so no, not really.

I would just recommend cleansing the ___domain from any systems you may have used it on and ensuring that you have no other technical ties the ___domain. Treat it just like any other ___domain you do not own.

First, let ArchiveTeam know, so that we can save anything public you have on the ___domain to archive.org so it will persist beyond the expiry.

https://archiveteam.org/

If you don’t own the ___domain then you have no say over what’s it’s used for. The only thing you can do is not to let it expire.