I'll try to be brief: the Archbishop of Canterbury has not underwritten that campaign. In fact, the movie is so horrendous from historical perspective that seeking any explanation of it on this sub especially is like asking Star Wars questions on NASA sub.

Now, if I recall it correctly, a person who single-handedly made the largest loan was Monmouth's own uncle, Henry Beaufort. However, he's never been the Archbishop of Canterbury. A colorful and remarkable person, his highest rank was that of a Cardinal.

Beaufort brothers (Henry's uncles) had very close relationship with him personally going back to his early teens and the Prince conducting military operations in Wales, as his father's lieutenant.

And Henry Beaufort, he was regarded as one of the richest, if not the richest person in England. His money helped Henry to continue the ruinous war.