Photoanalysisd using more than 100% of CPU

No, I am saying that it should have been there all along, at varying levels of activity depending on how much analysis there is to do on your photos and videos. Right after a system upgrade, Photos may need to apply new or revised analyses on your library; they can require a substantial amount of processing.

A process can show with more that 100% CPU usage because the usage is in percent of one CPU core, or one virtual core with hyper threading. Any Mac capable of running macOS 12 Monterey has multiple cores in its CPU. Most modern apps are capable on running multiple threads at the same time on multiple cores.

That's a background process to analyze the pictures in your Photos library. It should have been there in the past, for at least the last several releases.

Good work there :-)