One last step: grant Full Disk Access

Time Machine backups are protected, so Time Machine Display and its helper each need Full Disk Access. macOS requires you to grant this yourself.

1. Open Time Machine Display (in Applications). It detects what's needed and gives you a button to open the right settings — follow its prompts to grant the app access.
2. On the Overview screen, the Backup Timeline shows a prompt to grant the helper access. Click it, then drag tmdisplay-helper into the Full Disk Access list.

Per-backup sizes appear within a few minutes of granting the helper access. Everything else works as soon as the app has access.

To remove the helper later, run sudo /usr/local/libexec/tmdisplay-uninstall.sh in Terminal, then drag Time Machine Monitor to the Trash.