I think I may have isolated the problem at least for some iPhone models. This is only day one though.
Another poster commented about an issue with a SIM card and LTE which didn't make much sense to me except that if 13.4.1/13.5 contained a modem issue that was draining battery.
I had VoLTE (Voice over LTE) turned OFF but it seems that iOS 13's new menu system turned this back on. Turning VoLTE Off (Settings > Cellular Data Options > Voice & Data > LTE, VoLTE Off) seems to have improved the battery today although I have not used the device as much today. However, I am not seeing the dramatic IDLE battery loss as I was before.
It may be a starting point so please try turning VoLTE off and reporting your findings to all of us. If we find that this is the issue maybe we can submit a more detailed bug report. (For iPhones or perhaps iPads that have an LTE modem -- which would require LTE off entirely if this was the same problem)...
So, I have two suggestions:
Turn off VoLTE if you have the option. See how the device operates over the next 24 hours.
If you have an iPad/don't have a VoLTE option, turn off LTE and see how the device operates over the next 24 hours.
Let us know if this solves anything at all and then we may find the source of this bug.