EZ.... In reviewing the recent comments on the Peplink forum, it appears not all the 5G models have been certified for use by AT&T & Verizon. Supposedly this will happen sometime in September. I suspect this may be part of your problem.
With regards to T-Mobile, I believe the 5G models have been certified for use on their network.
Having installed multiple Peplink devices (no 5G models) with both Verizon & AT&T cellular plans, I have never encountered any issues if I was using a SIM with the appropriate data plan for the Peplink device. All the devices powered up & connected with the default settings from the factory.
Remove all SIM cards. You should be able to connect to the UI on the device via the Ethernet WAN port. Reset the device to 'FACTORY DEFAULT' & let it boot up. I believe from reading the string associated with your trials & tribulations, you have a T-Mobile plan. Insert this SIM in port A & make it the primary. Adjust any settings that are unique to the T-Mobile SIM & it should connect (takes a minute or two).
The attached is a cut & paste from the 5G Store, which clearly indicates AT&T & Verizon certifications are pending. Can it be made to work prior to certification, probably. I would be very surprised if the 5G store is going to help you to circumvent the lack of certification.
Good luck, once you get it working I think you will be very happy with it.