Facebook api – fbc parameter for Event Matching via Facebook Meta pixel not being sent

I have implemented the Facebook CAPI (via server side GTM) and in order to deduplicate the events being sent from the server and the browser, I need to send FBC via pixel and API.
I’ve found how to create the fbc (Click ID) parameter using 1st party cookie in GTM and added it to the GA4 (field name: x-fb-ck-fbc) tag which sends the signal to the server side GTM and to Facebook afterwards.

The issue I see is with the FB Pixel and how exactly to add the fbc parameter to it.

Some people seem to add FBC here:

<script> fbq('track', 'PageView', {'fbc': {{FBC Cookie}}} , {'eventID': {{Event ID}}} ); </script>

But FB does not seem to recognize it this way – in the Facebook Events Manager is still says that the FBC being sent are around 1%, which is too low.
From the Facebook Pixel helper I can see that the fbc is sent as Custom parameter:

And in the documentation FBC is considered an advanced matching parameter – it’s mentioned here:
https://developers.facebook.com/docs/marketing-api/conversions-api/parameters/customer-information-parameters

And here I can see that such parameters are added to the fbq(‘init’…):
https://developers.facebook.com/docs/meta-pixel/advanced/advanced-matching#implementation

So, I tried this as well. The Pixel helped now shows it sent as Advanced Matching parameter, but FB still does not seem to recognize it (amount of parameters sent is still 1%):

Anyone with a solution for this?