It says here:

May I become a Florida Notary if I am not a U.S. citizen?

Yes, you may become a Notary if you submit a recorded Affidavit of Domicile from the county clerk of the county in which you reside.

Here's what the form looks like

Nothing in there about USC or LPR status.

It looks like they use the IRS definition of "resident" - did you live more than 180 days in Florida last year? Did you pay Florida taxes? If you did, you're a resident.