I had the same problem. I also reinstalled Windows 11 while keeping apps & data and this fixed my problem.
HOWEVER this is only temporary. As soon as you reboot or I think after a few days it will revert back to the "bugged" state like it was before (slow indexing and 10% cpu usage for the indexing service). I reinstalled W11 twice now and the problem returned after a few days.
It's very weird because when I got it finally fixed there was almost no CPU usage at all and "Search Protocol Host" took up the most % of the CPU when idle (like 4% maybe?). Now this process is not taking any amount of CPU but instead the "Windows Search Indexer" process/"Windows Search" service which takes up about 9% usage all the time.
I gave up and just disabled indexing and use Everything to search files.