You absolutely want to have 1 TB free minimum for a 4 TB amount of data. If you can’t use Time Machine to exclude any files that don’t need to be backed up (exclude the /System folder and all system files as well as any database / cache files like outlook cached data) and then see how large the space grows.
Time Machine works best when you can delete files and have them saved for more than 6 months. If you’re not going to keep history, I would just do a sync / mirror using a product like Carbon Copy Cloner or Super Duper and rotate two drives in so you have one online sync and another that’s more distant.
As long as your data is static, and you don’t add or delete much, I would say 1 TB of free space would take about a year to get used up if you have normal small documents like papers, notes, some small photos coming and going and the bulk of the 8 TB is just a huge static library.
In your case - 4 TB free and 8 TB allocated after the initial backup seems like a very nice compromise. Within my totally unofficial “guidelines” and 50% room spare and reasonable size drives for the current size of HDD availability. A NAS or slower rotation drive would be fine if you want to save $$ and get the most space on one drive.
Since you tagged this video - you might instead have two buckets of data - and can optimize things. Don’t backup your ingest and working copies to Time Machine - just the project files and the OS files. Then have a second way to store and archive long term storage.
That’s more work though. If you can throw a pair of 12 TB drives and let Time Machine run A and B backups for a year - that might be a very good investment.