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If you have a release letter, you should probably send to credit bureau. I would go even further now that it is paid and see if the state comptroller's office is willing to vacate/withdraw the lien and then it can be removed from your profile.
The bureaus are quick to report negatives but don't always seem as quick on positives, IMO. It's in your interest to ensure they have the new info as quickly as possible so I'd let them know about it.
Love your goal card.
With PRs the CRAs may nor may not search public records themselves, typically a PR gets on your report not by the efforts of the CRA itself but by their purchase of info from companies like Lexis Nexis who send runners to the courthouses, country recorders, etc to obtain the information. If you have the release I would send it in with request for update. Good luck on getting those liens withdrawn