Finding AirPods Pro lost in closed case.

I lost my AirPods Pro and they are closed inside their case. Their last known location was at my work office Thursday lunch time, but I didn't realize they were missing from my pocket until Friday evening. My understanding is the last known location was likely just last time I opened the case and connected to them with my phone. So they may have gotten lost after I left work.

Interestingly, my phone say last location was Thursday lunch time at the office, but my computer says Wednesday at the office... I find it weird these would not be in sync.

My understanding if also that if they are closed in the case, I won't be able to connect to them to play a sound of use the "Find" function when I get close. Is that right? Seems like a pretty bad design. If I find them, I'll be getting an AirTag to go with the case. I've turned of "Notify when found" and marked them as lost. Any way to find them besides waiting for someone open them up? I've walked around and called around to all the places I've been with no luck so far.