I think algebraic effects usually just compile down to monads under the hood? As I understand it, it’s more like a cleaner interface to model side effects, than some new approach compared to the tools that haskell gives you out of the box?

No, not necessarily (that's just how some(?) of them are implemented in Haskell, and that's slow too). Since 9.6.1 GHC has primitives for delimited continuations, with which effects should be implementable in a more straightforward and performant way.

Alexis King, who added these primitives to GHC, on (delimited) continuations https://www.youtube.com/watch?v=TE48LsgVlIU

I had understood that the delimited continuations stuff was more like performance optimisation for the (slow) free monadic effect systems than a fundamentally different theoretical foundation for modelling effects in a pure language?

fwiw we also have fast effect systems in Haskell these days that are more like fancy type sugar on top of the ReaderT over IO style of things (effectful seems to be the most popular).

I've thought that all "native" (in the compiler instead of a library) implementations use (more or less) delimited continuations (some kind of temporary stack moving/copying). OCaml : https://github.com/ocaml-multicore/ocaml-effects-tutorial#3-... And Koka: I haven't found the paper/docs right now.

I know about effectful, but that doesn't use Reader (but provides one) but more or less directly IO (Ref) and "evidence passing", that's why it is faster than the other ones, the drawback is not being able to use non-deterministic effects and noo such thing as coroutines. But I talked about eff ("native" delimited continuations) should be more or less the same, maybe a bit faster, than effectful, but enable non-determinism and coroutines.