What's needed is to add a volume via Disk Utility to your external drive so that you can use it for non-Time Machine files too.
Here's an explanation from MacWorld:
"You can share the Time Machine container with volumes that aren’t being used for backups. Apple
notes in its Big Sur guide on a page describing the kinds of disk formats supported with Time Machine that the backup requires the whole “disk.” This appears to be an error: Apple really means that the disk can only have a single
container, which occupies the entire disk. The Time Machine backup, however, takes place to a single
volume in that container.
You can’t access the Time Machine volume directly through the Finder and store other kinds of data on it, but Apple states you can add a volume in the same container. This volume will contain regular data, and can be used independently of the volume assigned the Backup role."
(
https://www.macworld.com/article/36...atted-drives-but-there-are-a-few-catches.html)
Here's the steps I did to create the new volume:
1. Connect your external drive connected so that you can see it in a Finder window sidebar.
2. Go to Applications > Utilities > Disk Utility.
3. Select your external drive in the list.
4. On the right side of Disk Utility above the graphs, you'll see a Volume +-. Tap on plus to add the volume. You'll be presented with format and size options. I went with APFS and 10GB to test it.
5. The new volume will be created within seconds, and you can close Disk Utility. You should see it mounted in the Finder window sidebar below your Time Machine volume.
From there you can simply drag files to that new volume.
Hope this helps!