How do pages get updated checksum when switching page verification mode from torn page to checksum?
It won’t happen all at once. Each page will get changed independently when it is modified through some other action (e.g. insert or update).
This was done precisely so that this change would not be a size-of-data operation.
Of course you could force it to be immediate for a given table by rebuilding, but the big cost there would be the rebuild, since you’re writing all of the page contents anyway. Switching those pages to checksum as a part of the process is an almost-zero-cost add-on, like how much gas mileage you lose if you add a kid to the carpool.