I have a VZW eSIM for my postpaid line, and an H2OWireless (ATT MVNO) physical SIM. The VZW line is primary for voice & data.
I have occasionally seen the My Verizon app hang on startup (spinning graphic in the middle), but that may have been before using the eSIM+second SIM. In any case, force quitting the app and restarting it has worked reliably to get it running.
My current setup is T-Mobile postpaid on esim and Verizon prepaid on the physical sim. Nothing has worked to get the app working with my setup. I have force closed the app many times and even deleted the app and downloaded it again and nothing works. I am not very impressed with Verizon data speeds so I may switch to at&t prepaid for physical sim soon.