I can confirm it is the Google Services Framework ID you need to enter.
Before you can do so, you have to convert it from hex to decimal as the registration page only takes decimal values.
Entering your IMEI (as I tried, before converting GSF) will
not register your device.
Gemini works without registration. It was only after flashing LineageOS that I needed to register my device using GSF-ID.
After registering my GSF-ID, it took about 15 minutes before I could use GApps.
EDIT:
here's a guide, halfway down the article, on how to do this incl. links to apps and hex-decimal convertion.