Making room on my external hard drive.

You don't.

You don't delete items from the backup drive. You allow Time Machine to work as intended and delete older backups as required. To do otherwise risks corrupting the entire backup process.

TM deletes older files if they have been deleted from the source and when TM needs space on the backup drive for a new incremental backup. When TM finds it cannot free up enough space for a new backup it reports the disk is full. Then you can either erase the backup drive and start fresh backups, or replace the drive with another drive.

Please see:

Back up your files with time Machine on Mac - macOS User guide

Generally, you don't!

Time Machine should automatically remove old versions of files when a newer version is still available.

What's the exact error message?

Basically, yes. But until you have a second backup drive you can use for now I’d be wary of erasing my only backup even if it only for a couple of hours.

You do have other options such as using time machine itself to delete old backups (this won’t corrupt the time machine data) or running first aid via disk utility on the time machine drive in case it needs a corruption fix.

The ramifications when you erase the backup drive and start fresh backups is that you lose your old backups and for a short time between the erase and having backed up again, you’ll have no backups.

whats the exact error word for word. Any mention of snapshots?

(update: I see you quoted “"Back up failed. there isn't enough space on the G-DRIVE mobile USB” but Was that all?)

Hmm. It’s look that an erase may be needed.

unless... do you store anything else on that time machine drive apart from the Backups.backupdb folder?

Unlikely. It wouldn’t report that as a disk full error.

Time Machine deletes older files if they have been deleted from the source when it needs space on the backup drive for a new incremental backup. Time Machine "thins" it's backups; hourly backups over 24 hours old, except the first of the day; those "daily" backups over 30 days old, except the first of the week. The weeklies are kept as long as there's room.

How long a backup file remains depends on how long it was on your Mac before you deleted it, assuming you do at least one backup per day. If it was there for at least 24 hours, it will be kept for at least a month. If it was there for at least a week, it will be kept as long as there's room. By default, Time Machine backs up hourly. That cannot be changed in Time Machine. There are third-party utilities that will modify the backup interval such as Time Machine Editor.

The Time Capsule sparse bundle grows in size as needed, but doesn't shrink. Thus, from the user's viewpoint of the Time Capsule, it appears that no space has been freed, although there may be space in the sparse bundle.

Once Time Machine finds it cannot free up enough space for a new backup it reports the disk is full. You can either erase the backup drive and start over or get a larger drive.

Do, please, let us know what Apple say!