The "rise of power of the church" was not the cause of and did not exacerbate the collapse of Roman state power in the Early Medieval period. It was in fact in the Early Medieval that the Church was most instrumental in propagating and preserving knowledge.

Since you seem allergic to sources, here's a pretty good layman-aimed overview of actual up-to-date historical view of the arrival of the "Dark Ages" (i.e. the Early Medieval).

https://acoup.blog/2022/01/14/collections-rome-decline-and-f...

https://acoup.blog/2022/01/28/collections-rome-decline-and-f...

https://acoup.blog/2022/02/11/collections-rome-decline-and-f...

(From the narrative you put forward, I suspect your likely citation would be Gibbon. Who's... um... a bit out of date.)