How do you perform a proper time machine backup when you have existing data in the hard disk that you have saved

Sorry for the asinine question but I am pretty much paralysed with fear on how to do a proper backup without losing anymore data. My hard disk went blank and I managed to salvage the data with the help of apple tech stuff.

My current hard disk that I purchased in a moments urgency contains the files that I have saved. I would like to do a proper back up and what's holding me back is that if I were to use my external hard disk as it is, I fear that the files I have saved would be erased.

I was thinking of cutting and pasting the data from the hard disk into my laptop, with that, I have an empty external hard disk to begin the time machine process. I wonder if this sounds practical.

I read that there is a need to format the external hard disk but I am not sure. I am using Western Digital ready to use for Mac.

I read that it is good practice to encrypt the time machine, but I read that selecting this option will erase the external hard disk completely and hence the previous point on cutting and pasting the data into the laptop in the first place.

I am using Mac Catalina.

Would be grateful if someone points me to the correct direction on how to perform a proper time machine backup considering that I have a partially used external hard disk.

Take a look here: Does my Time Machine backup disc need to be dedicated?

My TM backup hdd also has other files. TM is in a directory that it makes on the first run. The issue can be the size of your backup. Is will grow over time. TM will remove old files when the hdd gets full.

When in doubt get an extra hdd. Your backup is worth the money. And after a few years it is wise to start again with a fresh hdd. Hdd don’t get better over time. Just start a new backup, don’t copy the TM data, it will take extreme amount of time and it does not help you in finding old files. You can open the old TM backup also.