How to transition Time Machine volume to a new Mac?
I'm about to migrate to a new Mac. Current Mac is running macOS 12 Monterrey and can't be upgraded, new one presumably will be macOS 13. Volume name of the startup volume will be the factory default, "Macintosh HD," on both Macs.
I plan to to the migration via WiFi transfer between the Macs, because past experience has shown that migrating from a Time Machine backup is excruciatingly slow, far slower than Mac-to-Mac WiFi.
Say the new Mac is up, running, and migrated. Let's also say I don't want to reformat the Time Machine drive and start from scratch, losing all the backup history from the old Mac.
I'd like to be able to attach the old volume and have the past history be recognized as the past history for the new machine so that I can e.g. recover month-old versions of files. I don't want to have Time Machine grind away doing a complete backup of everything on the new Mac, as if it were an entirely new volme.
What do I need to do to make sure that the old Time Machine volume is recognized as the "past history" of the new Mac? Does macOS automatically treat the boot volume on two different Macs as "the same" volume for Time Machine purposes?
Mac mini, OS X 10.11