Do you think that you will ever have reason to go back and recover something from several years ago that you've subsequently discarded?
I have a similar situation (and this is probably very common with Time Machine users). The Time Machine program runs in the background for month after month, year after year, and is only needed in the event that the primary machine hard drive fails and you need to recover. If that happens, at least in my own experience, most likely you simply recover to the most recent backup, you don't need to go back further in time to get something else.
The other reason for using backups, again in my experience, is if you install some new software and it causes problems. Or I suppose if you think that you have some kind of malware or something that has infected your Mac. Then you want to go back in time to a point before one of those things happened.
Long story short, unless you feel some need to keep the old backups, for some reason such as what I've mentioned, or some other reason of your own, might as well start fresh with the new Mac - keeping in mind that you don't want to wipe out the old backup in its entirety until you have the new backup safely in place. Since you seem to have several different backups, you're probably well covered.