Describe the workflow you want to enable

As partial dependence of a model at a point is defined as an expectation, it should respect sample_weight if someone wishes to use it (for instance, when you know your X does not follow the distribution you are interested in).

#25209 tries to solve this for method='brute' when you have new X. For older tree-based models trained with sample_weights, method='recursion' keeps track of the training sample_weight and calculates the partial_dependece with that into consideration.

But, as discussed during the implementation of sample_weight on the HistGradientBoosting estimators (#14696 (comment)), these models stores an attribute _fitted_with_sw and when partial_dependece with recursion is asked, it throws an error:

Describe your proposed solution

As discussed in #24872 (comment), the big difference between other tree-based algorithms and HistGradientBoosting is that HistGradientBoosting does not save the weighted_n_node_samples when building the tree.

Describe alternatives you've considered, if relevant

No response

Additional context

No response