I had the exact same issue...
I have an iPhone 7....my phone updated to iOS 13.5.1
Afterwards:
...'No Service' from my service provider. I was unable to make/receive calls, texts, or cellular data. I was only able to connect to WiFi.
I resolved my issue by resetting my network settings:
- Settings > General > Reset (at the bottom)
- Reset Network Settings
After I reset the network settings, the phone rebooted and when it came back up, the top left corner now said..... "Searching"
It didn't come up right away so I reconnected to my WiFi.
When I established connectivity with my WiFi, my cellular information kicked in.
I have no idea why it came up only after I reconnected to WiFi, but I'm not complaining.
Just to make sure it wasn't a fluke, I powered my phone off then back on......Service Provider information is still there.
Hope this helps