Is it possible to use `tmutil delete` or another command to delete one file from all backup intervals?
Here is a way to exclude folders from timemachine.

Hold the command key and type the space bar to bring up Spotlight.

Type Time Machine and open the system preference (not the application).

Click the Options... button in the lower right corner of the Time Machine system preference panel.

Click the plus button then navigate to the folder you want to exclude.

Click on the Exclude button.

Click on Save.


https://www.imore.com/how-exclude-files-time-machine-backups