Using external HD for backup (time machine) without erasing

You should read this: https://support.apple.com/guide/mac-help/types-of-disks-you-can-use-with-time-machine-mh15139/mac

"Note: The entire APFS volume is reserved for Time Machine backups. If you want to store files other than the Time Machine backup on the same physical device, use Disk Utility to create an additional APFS volume on the disk. The two volumes then share the available space."

As previously noted, the Time Machine destination disk needs to be APFS formatted. SO you have to reformat anyway. Which means you need to copy off all those other files from the external drive first.

The arrangement I recommend is:

• Separate disk for Time Machine backups of your Big Sur computer, that backup disk must be APFS
• A separate (from the Time Machine disk) disk for miscellaneous storage of files (videos, pictures, etc.)
• A third disk to backup the second disk used for miscellaneous storage

By the way, I would also recommend more than one backup disk for each of the disks you are backing up. Some people object to that due to the cost: my response is always, is permanent loss of "old videos, pictures, etc." worth it to save $100? Every single disk that you use, whether as the primary one or the backup one, whether SSD or HDD, will eventually fail someday. It is a matter of when, not if. These failures start to happen after 3-5 years of constant use, some last a lot longer, some shorter.

A 4TB rotational drive that has been used for several years in a Time Machine/another data role, probably should not be trusted to place new Time Machine data on it. If it were me, I would start with a new drive, because everything would be lost if the older drive failed.

Personally, I only use a Time Machine drive strictly in that role only, and do not store other files on it.

from your description of what you want to do, unfortunately, a new HDD is very likely in your future. you could either use the new drive as your new TM. or buy an HDD with just enough room for your existing data, transfer that data to the new drive, then erase and format the 4TB as your TM drive. or use your existing drive for external storage, and buy a drive 2 to 3 times the capacity of the MBP's internal drive and use it as a TM. either way the TM drive needs to be formatted APFS which if done to your existing drive, the data on it will be erased.