Add will be disabled if you have selected the physical disk. Select the container disk or the existing TM volume instead (assuming the disk is APFS formatted) and you will be able to add another volume alongside in the same container. As you are aware, they will share the free space in the container and this will affect the TM housekeeping and retentions over time.

Ensure View | Show All Devices is selected to show the container disk. Then Cmd-Click on the container disk underneath the physical disk and Add APFS Volume... The other alternative is to click + Volume in the toolbar. If your TM volume is encrypted, then this will not apply to your new volume, and you’ll need to specify APFS Encrypted if you need to in the resulting dialog.

Also worth checking is that the added volume appears automatically in the Time Machine exclusions. Otherwise it will be doing a backup from one vol to another.

Tested on macOS 12.6