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