delete folders in time machine

Truly new Macs do not come with the drive partitioned ... it's all one single volume. If your Mac came with more than one partition on its internal drive, it's used; not new.

Erase the backup drive and reestablish it as a Time Machine backup. Assuming you migrated its data to the "new" Mac (that's one reason backups exist), the current dataset is not needed any longer and you can start over.

your backup drive needs to be 2-3x your internal's drive's size.

If you're saying there is insufficient space on the internal drive, you need to open up space there ... 15-20% of the drive needs to be totally united 100% of the time. But this condition should not be present on a truly new Mac. At least not immediately after purchase and initial setup.

Free up storage space - Apple Support

Good luck

<< but I gained 2GB/folder on the Seagate. >>

You have completely TRASHED your old backup by doing that, so you really should completely ERASE the drive and start over.

... and while you are trashing things, Cocktail should be on the list to GO.

Since you don't need the old files, use Disk Utility to reformat the drive.

Start over with a fresh new TM backup.

Erase the drive as suggested.

D.I. Johnson has the best answer.

There is sometimes the Option to "inherit" your previous backups, and continue along the same path, but is is not always offered automatically. If needed, readers can look up some Terminal commands to make that inherit process more likely.

You also have the option at any time of adding an ADDITIONAL backup drive to your backup set, and every other backup will go to every other drive as long as both remain available. Each backup drive is independent of the other, and the newly added drive will do a new full initial backup as its starting point.

Time machine maintains a complex database of strongly linked files on the backup drive. Rather than store additional copies of unchanged files, a LINK to the previously-stored copy is used.

Time machine strongly protects against deletions using Finder, because allowing deletions without consolidating the changes inside Time Machine would damage the Integrity of your backup set.

You can't easily delete Time Machine files, but if you somehow manage to do so, you will wreck your backup set.