- Turn off Low Power Mode.
- Reset > Privacy & Location Services > Find My app
- Toggle from "While Using" to off, wait 2 seconds, toggle back on
- Toggle from "Precise Locate" to off, wait 2 seconds, toggle back on
- Wait 20 - 30 seconds, then Open FindMy.app
My case had fallen out of my jacket pocket, and I was unable to find it, thinking it was in the car, however after some time, I had physically located the case sitting on the floor near my jacket. WITHOUT touching the AirPods Pro Case (Lightning version), I found this forum post, and read about resetting the Privacy and Location services.
The ear buds were at 18%, last time they were in the case was 4 or so hours ago. Once FindMy "polled the network" at which point, Find My did a new review of the surrounding items, and the Case showed up, even though the buds (both L and R) were sitting on my desk.
Another guess is that in Low Power mode, which both my iPhone and iPad were in, was delaying the FindMy updates from happening. The RESET of the Permissions for Privacy came from another post that I read.
The reset instructions above required NO restart from my iPhone.
Good luck.