Hi,
I just tried using Sync to sync to an android phone. The phone is running without GApps, and displayed a warning that Brave cannot work without google services. I can confirm that Brave works just fine, but I was wondering if the Sync feature would work without GApps.
Did you try to install MicroG?
This may could help. 
It is what it came in my mind in seconds when read these posts. I could be wrong, though.
I could
But that would kind of go against trying to avoid google services. I am more asking if there is any known hard dependency to google services that are required for the sync feature
@onlinepersona yes – at this time, Google Play Services are required in order to use Sync on Android.
I’m with you, I do have also a rooted/degoogled phone, though the amount of influence google has on android you got not around to have a small piece of Google services installed. At least it’s open source and you know the code.
If you don’t want to leave under a rock, you need google (play) services or at least MicroG because many apps are depended on this — of course it depends again on the app you want to install a few one can live without google (play) services, but they mostly also use more battery by the way when they have a notification services running by their own like in messaging apps.
I do not like this either, but many apps don’t or do work only limited without those services installed. 
I would recommend installing MicroG for some specific situations, but at the end it’s your decisions and I see your point. 
It’s not that hard:
Here is the wiki: MicroG Wiki
Here are the Download possibilities: Download Page
I recommend reading through the wiki at first and then downloading the package. On the download page you have the possibility to download via F-Droid repository or further down via direct download.
I hope this helps. 

In that case maybe I’d rather live under a rock @LxWulf
It’s ok I don’t need Sync that bad.
I will mark your answer as accepted though, as for most people this would be the way.
Additionally, this could be a option for some if they wish to run Gapps https://grapheneos.org/faq#google-services
Thanks for the clarification ! I will mark the answer recommending MicroG as the solution then for those who would come accros this later 