Your OP attempted to prove that the incident of Acts 25:7-11 meant Paul "considered religious issues the [de jure] right of the powers that be."
It was a de facto reality that Rome would become involved under then existing Roman law and the use Paul's accusers made of it.
That Rome had claimed the right and ability to make such decisions does not mean they had the de jure right to do so.
The fact is, Paul appealed to this authority; would he have appealed to a court of right if he did not believe the court had the right to judge the matter? Of course not.