Deleting Time machine backups on LaCie external

The feature that is described in KiltedTim's link is no longer available in Time Machine. This is all you get when you Control (right) - click on a file in Time Machine:

It's not possible to remove backups anymore. If you try to drag the file to the Trash bin it won't empty and will stay there until you erase the drive and start over new.

Unless there are files in the backups that are currently not on the boot drives you can erase the drive and start over from scratch. Just be aware that the first backup will take a long time so plan on letting it run overnight.

Time Machine is supposed to delete the oldest backup when it needs room for new backups. You'll get that message if you don't have enough room on the boot disk you're backing up to store a local snapshot. How much free space do you have on your boot drive?

TM Backup Utility marks the Drive as READ ONLY and only TM Backup Utility has the ability to remove Older Snap Shot and has that ability as previously mentioned.

You maybe better off putting this drive aside for safe keeping

Then Purchase another Drive with at least 2 1/2 Greater Capacity than the Combined Total Capacity of the 2 Computers you plan to use this drive for.

Personally, I would purchase 2 Separate Drives and use 1 for one machine and the second for the second machine

Putting ALL the EGGS ( 2 Computer TM Backups ) in 1 basket ( drive ) and the Basket Fails - then Both Computers are exposed to losing Important and Non Replaceable Personal Data

You have to do it from inside of the Time Machine interface.

https://www.cnet.com/tech/computing/how-to-clear-unwanted-files-from-time-machine-backups/