Resume prior Time Machine and Carbon Copy Cloner backups with new computer?

A late 2009 iMac was erased and set up as a “new” computer running under macOS 10.13 (High Sierra). A Time Machine backup (on an external USB hard drive) from a slightly older computer, an early 2009 iMac, that ran under El Capitan, was restored to this “new” computer. The “new” iMac, restored from the “old” iMac, runs well.

Should I start a new Time Machine backup for the “new” computer? Or can I just continue the original TM backup on the same external hard drive, thereby retaining access to older backup files?

Similarly, is it proper to “continue” a Carbon Copy Cloner backup of the “new” computer on the same backup that came from the older computer? The computers are different, of course, and the older computer ran under El Capitan while the newer computer runs under High Sierra.