They wont sell you the SIM true, but they will swap it for you if you bring in the old SIM.
You can just order and pick up the LTE modem at any service center just send a email to:
[email protected] and ask for part :
1054968-01-B PCBA, LTE CONNECTIVITY, UBLOX GPS
(for EU the part number is: 1054968-02-B PCBA, EU LTE CONNECTIVITY, UBLOX GPS)
Mind you these are freely available over-the-counter parts, not restricted in any way.
Look it up on
https://epc.tesla.com/#/systemGroups/53890 , it clearly says "Over-the-Counter(No VIN)"
After you swap the modem test if the MCU gets LTE signal, if so then you're done and you can assemble the dash etc.
If not then take out the SIM, drive to the service center again and ask them to swap the SIM card for you while showing the invoice for the new LTE modem so they know your request is legit.
In some SIM swap cases it could be necessary to have the APN configuration changed (this info is stored on the MCU). Tesla can do this remote if you hook up the car to Wifi so they can get in. Or they can do this from their service Toolbox laptop within minutes. They might charge a few $ for the procedure, but it is pretty trivial to do so.