According to the OP, this info is needed if they want to request a vote-by-mail ballot, so isn't this info just part of the vote-by-mail request form?

The request for a vote by mail requires the voter to give either their Florida Driver's License number or the last 4 digits of their SS number. The Supervisor of Election gets this information from the voter, not government agencies. Notifying the voter that the SOE is not in possession of this information gives the voter the opportunity to provide the information and become eligible to order a mail ballot.

My understanding is that the information provided has to match information already provided on a voter registration form. Long time residents may have been registered before that ID information was required, hence is not on file. My Supervisor of Elections sent out similar notices at least a year ago. She was a long time resident and was one of the voters who had to provide that information. If there is a suppression element it would be that the notices are being sent out so close to the start of voting for the August primary.

I suppose the justification is that it is easier to look up a local file rather than run confirmation through an external government agency. Vote by mail requests can also be ordered by phone. Our local party sends out robocalls, text messages, emails, and postcards prompting Democrats to sign up so that the Supervisor's office is prone to receive such requests in inconvenient clumps.