Time Machine doesn't see Time Capsule

We assume that you have.......

Powered off the modem/router

Powered off the Time Capsule

Waited a minute

Powered up the modem/router again

Waited a minute

Powered up the Time Capsule again.......correct?

On your Mac.......Open Finder and look on the left panel of the Finder window to see the Locations heading

Does the Time Capsule appear under the Locations heading?

If not, it will probably be necessary to reset the Time Capsule and then set it up again. This will not affect any of the stored data on the Time Capsule hard drive.

I set up an old Time Capsule here as a test with a Mac running Sequoia.

When I open System Preferences > Time Machine and click on the + (Plus) button at the bottom of the Time Machine window, the Time Capsule appears as a destination to select for Time Machine backups.

I am unable to duplicate your report of only the Mac's hard drive appearing as an available backup destination, and cannot recall ever seeing this type of option in Time Machine.

Nice work! Glad that you got things working!