What’s the advantage here of using effects over monads? It seems to me that all the proposed benefits of effects are reproducible/reproduced already by monads. Is it simply to get stateful actions while still being pure in a dynamic type system rather than static?

Better ergonomics, direct style syntax, no need for monad transformers. There might be second order advantages like small performance gains compared to monadic effects.

My understanding is that monads can only be composed in specific orders or not at all without monad transformers.

The "algebraic" part of algebraic effects is that the effects also come with implicit compositional rules that say how you can put them together. You can design a family effects with rules like commutativity and associativity, so that you can be sure of how to compose them.