How do I create a new folder on an APFS external drive that is also used for Time Machine backups?

the only way to do what you want to do would be to partition the drive into two (or more) partitions BEFORE assigning one of the partitions to TM. reason being is that otherwise, TM wants the whole drive for itself. with big sur, the only thing that can write to the TM drive is TM itself. you also need to format it as APFS because big sur requires new TM drives to be formatted as APFS.

With APFS, partitions are now called containers and containers can hold multiple volumes. With TM, the APFS volume is assigned the role of Backup, and should not be used for anything other than for TM backups.

If you want to store other things on that drive, you have two choices:

1. Create an additional APFS volume in that container, or <== this would be the preferred method
2. Create an additional container with the number of volumes you need.

Here's some "light" reading material that you may find informative:

• Time Machine to APFS: Evolution - The Eclectic Light Company
• APFS changes in Big Sur: how Time Machine backs up to APFS, and more - The Eclectic Light Company
• Time Machine finally gets support for APFS in macOS Big Sur - Macworld
• The Issues with macOS Big Sur, Time Machine, HFS Volumes, and APFS - OWC

you're welcome. :)

You can create an APFS Volume instead of a partition, but you have to create it in Terminal using diskutil. You can set a quota on the volume to restrict the amount of the drive it will use.