Time Machine Backups of External Drives When Changing Macs

Good day to you all –

I have been running an M1 iMac with a 4TB external SSD being used as direct access storage, and I use Time Machine to back up that external SSD to two external 5TB HDDs once a month. I don’t even backup the Mac’s internal SSD, just the external SSD where I keep all my data.

I am switching now to a 16″ MacBook Pro (M1 Pro) and am wondering:

Is it possible for my MB Pro to pick up where my iMac left off with the TM backups? Or do I need to wipe the two HDD backup drives and re-initiate the TM backups of the 4TB SSD through TM on the new MacBook? It would stink if every time you bought a new Mac, you had re-do several TBs of backups like this.

Thanks for your help!