How to get tmutil compare to show results deeper than root directory
This tool is designed to operate on the entire backup set. Rather than try to bend it to your will, may I suggest a tool that does precisely what you seek, does it fast and in the background and can even help you track changed files when your backup drive is not mounted.


https://www.soma-zone.com/BackupLoupe/


The loupe tool works best for me when I track deleted files, so once you get a couple of your recent backups scanned, you can explore what’s changing hour by hour or day by day. There’s no need to let it run over dozens of backups for you to get a feeling if it will work well for the question you pose here. Long term, you’ll want to decide if you let it index in the background and keep the indexes always up to date or launch it only when you want deep scans and then let it run to get your analysis up to date.

Due to the limitations of tmutil compare this tool implements their own scanner since as you point out, the main tool is good to know the entire change load and not focus on specific parts.