It can take anywhere from 10 minutes to 1.5 hours, it depends on things like
How many messages you have
How much storage you are using on your iPhone and desktop
Your internet speed
If you disconnect your phone or your phone or laptop runs out of power
Once we start looking for messages, you’ll see this screen, which estimates how long you have left. Generally speaking, it takes much less time than the estimates it makes at the beginning of the search.
Resources
Talk to a human here