If its an external drive it may be excluded.
Go to the Systems Setting-> Time Machine
Click on Options and make sure that your storage drive is not showing up in the exclusion list. For instance, my data drive is, as its an external drive.
So if it fails suddenly tomorrow, what will happen?
Every file that you want to keep needs to be on 2 separate devices -- at least.
I've literally just been replying to a thread on another forum where someone was asking how to recover data from an SSD, because it had just failed, and they had no backup.
The external disk must also be in APFS or Mac OS (Extended) format in order for Time Machine to back it up. I see a lot of external disks using exFAT, sometimes because they need cross-compatibility with Windoze and other times because ¯\_(ツ)_/¯
If you have no data of your own, only copies of other people's data (like games and downloaded movies), then you have nothing to lose. Having "nothing to lose".... Is that a bad thing or a good thing? I don't know.