One massively under-appreciated item that runs after a major upgrade is Spotlight Indexing. In activity Monitor, you will see tasks like mdworker and mds using processing power and some I/O.
Initially these tasks are re-computing the spotlight index, which make searching for items on your Mac really fast.
If this activity persists beyond a few hours of awake and not busy time, the activity may be based on the other use for mds and mdworker. These tasks are very important for using Time Machine.
The recommended size of a backup drive is at least 2.5 times the size of what needs to be backed up, for long-term, trouble-free operation. This is now the Trouble implied in that statement. Immediately after a major upgrade, your NEW Full backup needs to go onto the drive where your OLD Full backup and many incremental backups have already sprawled all over the place.
Your system may be working VERY hard to consolidate (NOT DELETE) older backup instances to make enough space for a NEW Full Backup on that same drive. It may take quite a while [of Awake and NOT Busy time] to get the old backup instances thinned down enough so that the NEW Full backup can be added to the backup drive.
If your backup drive is far smaller than recommended size, this can be like two elephants trying to pass each other in a narrow hallway.
things to check for:
• can you do spotlight search? or does it tell you, 'try again later'
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system Preferences > Time machine
• Has your first Backup since the Upgrade completed to the Backup Drive?
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