(Evan can’t answer)
I’ve noticed in a couple games that I’ll find a magical catalyst outside of the room with the alchemy pot, and sometimes I’ll also discover a hidden secret room with an extra alchemy pot and usually two bonus energy crystals in it.
Is it implied that when you find a loose catalyst there is probably also an alchemy pot room in that level?
No, they don’t. Every region has two strength pots and three upgrade scrolls. Demon Halls are no exception.