My Time Machine disk is full and it will not delete anything even though I have that option selected.

You can erase it by using Disk Utility in Recovery mode:

About macOS Recovery on Intel-based Mac computers - Apple Support

Use macOS Recovery on a Mac with Apple silicon - Apple Support

Put this Drive aside for Safe Keeping ( like Safety Deposit in Bank ) for Future resting of specific files.

Get another External Drive with 2 1/2 Times Greater Drive Capacity of the Internal Drive and setup a new Time Machine.

Read If the Time Machine backup disk for your Mac is full - Apple Support