Actually, this will not work as because you have an in-memory record, so only the record ID is sent back to your code and everything else like trigger code, formula fields etc. you will not see immediately. So, you need a query to see these fresh values you can try something like :
Case newCase = [SELECT OwnerId, ANN_Accepted_From_Queue__c FROM Case WHERE Id = :c.Id];
I hope this will help.
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