I would not erase the Mac mini yet.
Since Migration Assistant reports insufficient storage even though the Mac appears to have enough space, first compare its stated storage requirement with the Mac’s total capacity and available storage.
In macOS 15.7, go to Apple menu > System Settings > General > Storage and allow the calculation to finish. Note the Available amount and total drive capacity, then compare them with the requirement shown by Migration Assistant.
Also check what Migration Assistant is transferring. If it includes unnecessary user accounts or large amounts of data, reducing what is selected may resolve the problem. Restart the Mac and try the migration again.
If the problem persists, consider starting the Mac in macOS Recovery and using Disk Utility > First Aid to check the internal drive before considering an erase.
Before erasing anything, verify that the Time Machine backup is accessible and contains the important data. A Time Machine backup provides files and information for restoration or migration; macOS itself is installed separately.
If Migration Assistant still cannot complete after these checks, erasing the Mac and reinstalling macOS is an option, followed by another attempt to migrate from the Time Machine backup.
Apple’s instructions: Migration Assistant and Erase and reinstall macOS.
If you provide the Mac mini’s drive capacity, Available storage, and the storage requirement reported by Migration Assistant, the discrepancy can be assessed before deciding whether an erase is necessary.