3g/4g USB dongle not showing up

No, you are not doomed. Anything can be fixed. We just need som details to figure out exactly how.

First, please post the output of
cat /sys/kernel/debug/usb/devices
as mentioned on https://openwrt.org/docs/guide-user/network/wan/wwan/ltedongle . This will show the device ID and the configuration before modeswitch. Not all modems require modeswitching so it's always good to start exploring the options here, even if eject might work.

The /dev/sda device sounds like your modem might have a card reader. It can't be the fake CD expected as a mode switch device. So I guess eject won't do any good. Anyway, you need to installe the eject package to get the eject tool.