Sync API is cumbersome (in my opinion)

If my understanding is correct, to add a sync function to a GenericSplitFunction, you need to overload synchronize_solution_with_parameters!(integrator, params, sync::MySync) where MySync is some type the user must define. To be concrete, at minimum I need to define all the below:

struct MySync end
sync = MySync()

function OrdinaryDiffEqOperatorSplitting.synchronize_solution_with_parameters!(
    outer_integrator::OrdinaryDiffEqOperatorSplitting.OperatorSplittingIntegrator,
    ::SciMLBase.NullParameters,
    ::MySync
)
    @info "Sync called at time $(outer_integrator.t)"
end

I feel this is a bit cumbersome and would like to suggest just a function-based approach where the user just needs to supply a function directly such as

my_sync(outer_integrator, params) = ...

We would just need to add

function synchronize_solution_with_parameters!(outer_integrator::OperatorSplittingIntegrator, p, sync::F) where {F<:Function}
    sync(outer_integrator, p)
end

and we could still keep the other way as well. This should be OK since the functions should be known at compile time.

Am I missing something why this can't work? Or will hamper other wanted behavior?

Start at the synchronize_solution_with_parameters! entry point for OperatorSplittingIntegrator and inspect how GenericSplitFunction dispatches synchronization types. Check the existing method and surrounding API behavior before assessing the proposed function-based overload. Done means determining whether the overload preserves current dispatch behavior and documenting or implementing the accepted approach.