can you go into the time machine and remove previous backups in order to free space on the external hard drive

No, because that backup might contain a file that has not changed in 10 years. It does not get put into newer backups.

But, don't worry, if Time Machine runs out of space it will delete the older ones for you, safely.

"The oldest backups are deleted when your backup disk is full. "

Back up your Mac with Time Machine - Apple Support

If you are using an HFS+ backup setup prior to Big Sur, you can remove items from the Backup using the Time Machine interface.

Find a file or folder in the backup, ctrl-click on it, and remove it. The only reason that would be feasible is if you knew you had a bunch of very large files you don't care to ever restore.

If the backup was started in Big Sur or later, you cannot delete anything manually.

Because of the way the backup is made, deleting what you think is an "old backup" may delete nothing at all. Or, it could delete everything. Each of the folders in the backup is not a complete copy of everything backed up before it. It may look like it, but it is not. The vast majority of the items you "see" in each folder is a hard link to the last changed copy of the item. That hard link takes up essentially no space, so deleting it would not increase the space available on the drive.

The best way to recover space on a backup is to delete the backup and start new. That will pare down the backup to what is currently stored on your Mac. That will then grow as changes to files are made. Note the limitation of not being able to delete individual items from a backup like you could if you maintained the legacy backup scheme.