I have never understood why people using MicroG can use apps like SNCF-Connect, while I cannot.

SNCF-connect is the largest online marchant in France. Since june, I cannot click the "pay" button anymore. It coincides with the new feature of Pay with Google.

So : is it because MicroG allows calls to Google services on e/OS devices, while my LineageOS refuses ? Or because MicroG implemented a try catch around this call, without any call to Google's servers ?

I think that's because /e/os also distributes App Lounge [1], which can connect to Google Store and handle payments (most of the time).

[1] https://doc.e.foundation/os/apps/app-lounge/

If it connects to Play Store, then isn't that the same as Aurora? Can people's accounts be banned? That would really suck to pay for something and lose it because Google banned you haha!

It really sucks but there is no other widely supported standard for in-app purchases. Some services refuse to use credit/debit cards payments for some reason.

I've been using Aurora for almost 6 years with no issues

it use aurora source code

Some Play Services calls are stubbed out as no-ops and others are reimplemented either with fully free replacements (e.g. navigation) or else by calling proprietary Google remote endpoints (e.g. firebase)

I have no Google anything installed on GrapheneOS and SNCF Connect works fine.

Are you sure? Login doesn't work on mine, and language is stuck to English idk why

Try the per-app exploit protection compatibility mode. That's generally the first thing to try, especially for apps with dubious anti-tampering code. If it works then it can be narrowed down to the specific exploit protection and should usually be reported to the app developers. The default enabled exploit protections for user installed apps have no false positives and neither does memory tagging (MTE).