Related problem: I'm using the native keyboard and a Logitech bluetooth mouse. There is a lag in the search function within a folder window such that if you click the spotlight there and start typing, the second letter of the word is the first letter that shows up typically.
At times this seems keyboard-related but at least for the folder search may be related to a lag in populating the free text search box after clicking the magnifying glass.
Using the spotlight search tool (F4) has no lag.
16" MBP, 12.0.1 Monterey