A colleague asked for help. She had installed Keyman 14 on her Mac (MacOS 12.01) but was not able to select it to use a keyboard. When I got on her computer, I found Keyman mentioned in the permissions settings, but it was not listed as an input source. I was able to add it by clicking the + then finding it in the list under Multiple languages.
On my own Mac, I had not yet upgraded to Monterey so I removed Keyman, then upgraded to see if I could then install Keyman and reproduce the incomplete install. When I installed Keyman, it asked if I wanted to add it as an input source, and did so without a problem. Maybe the colleague had not given this permission when she installed it the first time?
I guess the conclusion is Keyman 14 works fine with MacOS 12.01, but missteps in the installation are possible.