Solution 1:

Computing some checksums is not a restore test.

Restore databases for real. Prepare (test) database servers. Restore data, timing how long it takes. Connect test application servers, if available.

An outline of such a restore is in Azure DevOps Server documentation, although details likely need customization to your environment. In particular, whether the restore wizard can handle some details for you:

If you manually configured your backups, you cannot use the Restore wizard in Scheduled Backups to restore those databases. You must manually restore them using the software you used to back them up.

Unfortunately, restore of a general purpose, multiple tier, database application like this can be a bit of work. Encourage leadership to do restores regularly, at least on major infrastructure changes like a new backup system.