The setup assistant does not give you the option of opting out of specific types of content on the Time Machine backup and Migration Assistant does. If I am going from an Intel Mac to an Apple Silicon Mac, I may choose to use Migration Assistant after the operating system installation so that I can exclude any third-party Intel applications from being installed.
If am upgrading from Sonoma to Sequoia and from an M2 Mac Mini Pro to an M4 Mac Mini Pro (as I have done), then I likely will use the Setup Assistant with the Sonoma TM backup for this purpose as there are no third-party applications that I choose to exclude.
In either case above, I start a fresh TM drive for the first backup of the new operating system and never let it use the previous TM backup drive again.