How do I fix mobile broadband/WWAN with Quectel EM061K-GL on ThinkPad T14 Gen 5 21MC (AMD) running Ubuntu 24.04.1?

I just got a T14G5-21MC and installed a fresh copy of Ubuntu 24.04.1 on it. It was unable to see the Qualcomm FastConnect 7800 Wi-Fi adapter at first, but a kernel update addressed that (had to search and install 6.11 from official apt repo). However, the mobile broadband still isn't working.

I attempted to enable it with mmcli -m 0 --enable but I get couldn't enable interface: 'Invalid transition'. I read somewhere this was about the card being FCC-locked, so I downloaded the script from the Lenovo support to unlock it, but running it did nothing helpful. The status report still reads

  Status   |                    lock: sim-pin2           |          unlock retries: sim-pin2 (10)           |                   state: enabling           |             power state: low

despite it not being PIN-locked.

The following commands did not help:

• mmcli -m 0 --reset
• mmcli -m 0 --set-power-state=on
• sudo rfkill unblock all (hard and soft blocks were already off)
• sudo systemctl restart ModemManager

Starting to get in over my head here. How do I make this work?