No service on Blackview BV 5500 Pro with Lineage 17.1
Update
So, actually, I've tried to install magisk, which I believe is the culprit.
Following the documentation, since this model does not have Ramdisk memory, I've patched the recovery.img file using their Manager application, and then flashed my recovery partition, using
 fastboot flash recovery /path/to/magisk_patched.img

After rebooting, their application was still not detecting magisk's installation, and my OS could not detect my SIM card anymore.
After flashing back the stock recovery, the sim card was back.
This seems to be a fairly common issue, judging by

https://github.com/topjohnwu/Magisk/issues/2201
https://forum.xda-developers.com/mate-9/help/sim-card-reading-failed-magisk-xposed-t3819966
https://forum.xda-developers.com/apps/magisk/problem-sim-card-detected-constant-t3860135


Original Message
Ok, so I've done the following:

Installed the official rom, BV5500Pro_E535_V1.0_20191105V6, that blackview shared directly with me: the sim card was not even recognized!
Flashed everything, installed a previous version of lineage (lineage-16.0-20191017-UNOFFICIAL-treble_a64_bvN): sim card still not recognized.
Installed another official rom (that they share here, called BV5500Pro_EEA_E535_V1.0_20190514V8): the sim card is back, and I can connect to the network!
Re-installed lineage-17.1-20201012-UNOFFICIAL-treble_a64_bvS. The sim card is still detected, and I can now connect to the service!

Needless to say, I have no clue what actually solved my issue.
My network is set to GSM / WCLMA / LTE (PRL) and I have not noticed any value or configuration that would have changed…