Can I limit the amount of space used on my external hard drive for backups? Or will it only keep adding more backups until the entire drive is full? I want to save some space on the hard drive for other things in the future.

In Time Machine, can I limit the amount of space used on my external hard drive for backups? For example, limit to 10 backups? Or I year of backups?

Nope.

After a while you may want to completely erase a backup drive and start anew though. A TM backup will eventually contain many millions of little files, making it time-consuming to transfer those backups to another drive for whatever reason you might want to do that. And if you wanted to use Disk Utility's First Aid, it will take a long time to finish with that many files.

That's why it's best to have more than just one backup drive. Erase them once every year or two. Just not at the same time.

Or will it only keep adding more backups until the entire drive is full?

Yes. Once it approaches its capacity limit Time Machine will begin to remove old, "expired" backups. TM will tell you when it begins to do that. It's normal.

I want to save some space on the hard drive for other things in the future.

Do not use a Time Machine backup drive to store other, non-Time Machine files.

Yes, you can limit the space a TM backup takes, at the level of the drive partition.

Time Machine will fill up all the available space on the partition you use for the backup. If you want to store data on the drive other than the Time Machine backup, you can use Disk Utility to create separate partitions on the drive [note: you must format with MacOS Extended (Journaled), not APFS, for TM to work under Catalina; I think Big Sur TM can use an APFS drive]. The different partitions will mount as separate drives, and you can select the one you want as a TM backup (a good rule of thumb is a backup capacity of ~2.5x the amount of data you need to back up, which is ideally not more than ~80% of your internal drive capacity).

For example, I have a 5 TB external drive on which I have 5 partitions of different sizes, four of them are used for TM backups of 4 Macs in the house, and one partition is to back up other files.

As a side note, if a file is on your internal drive that's backed up with TM, there's no point in storing that same file on a different partition of the same drive you use for the TM backup, and if that file is not on your internal drive but only on the one external drive, where is the backup for that file? In my case, I have a 10 TB NAS for local TM backups in the house and storage of family media that's not on anyone's internal drive; the 5 TB external drive is for an offsite copy of those TM backups and the family media.

Additionally, you should not really have all of your backups on the same drive because all drives will fail at some point. In that case, you would lose everything. I prefer having more drives with smaller storage size, so each one has its own drive. It's a bit more hassle to plug in/unplug, but I feel better with that and I have everything backed up at least twice on different drives.