After a major update, your Mac needs a certain amount of "awake but not too busy" time to do two things related to Spotlight Indexing.
• recompute the idea of metadata including every word in every document on your Mac, to make spotlight indexing reasonably fast.
You can see if it is done with this part by asking it for a spotlight search. If it is not ready, it will tell you it is not ready, wait a while.
• update your Time machine backups. This depends on first completing the Spotlight index, because that index is used to make backups reasonably fast.
To check if that has completed, use time machine preference pane to check the status of your most recent backup. if it has completed a backup since your software update, the delays and freezes attributable to that cause should cease, and we will have to look for other things.