There is no requirement for the FSW to be a resource of the AG and you should see no detrimental affect from removing it. The FSW will remain a resource of the CCRG.
Here is a guide I have used in the past for deploying an FSW:
https://learn.microsoft.com/en-us/windows-server/failover-clustering/file-share-witness
An FSW can be used on multiple clusters for high availability.
I hope this answers your question.
Thanks.
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