How to Check if Restore is Taking Place.

You can check the progress of vbr restore on the vertica node where you started the process. the progress percentage will be printed on the screen
Example output of vbr restore:
vbr --task restore --config-file db.ini
Copying...
1871652633 out of 1871652633, 100%
All child processes terminated successfully.
restore done!

Other way to know is reviewing vbr.log, it should be present at the path which has been set to tmpDir in your ini file.
https://www.vertica.com/docs/9.2.x/HTML/Content/Authoring/AdministratorsGuide/BackupRestore/RestoringFullDatabaseBackups.htm

Thanks for the quick reply. I forgot to mention that I will want to know if restore is running and its progress when I'm not the one who initiated the vbr restore command and do not have the command line progress.

In that case, You can check vbr.log by logging into vertica node and check if any rsync process is running in vertica node. vbr uses uses rsync internally for backup/restore.