Does converting continuous variable to discrete(categorical) variable increases accuracy of a tree based model?
I actually agreed with the now-deleted answer: you're unlikely to see improvement (at least with any consistency).

As you point out, binning a continuous variable just reduces the allowable split points for a tree model.  This reduces the capacity of the overall model.  That may be beneficial or detrimental, depending on how it affects the bias-variance tradeoff: I would expect it to help a lot on a fully-grown single decision tree, but probably hurt a little in a well-tuned ensemble of trees.

There are two nice examples in the sklearn docs illustrating their binning preprocessor:
https://scikit-learn.org/stable/auto_examples/preprocessing/plot_discretization.html
https://scikit-learn.org/stable/auto_examples/preprocessing/plot_discretization_classification.html

Extending the second one to (1) also include a full decision tree and (2) add binning-then-nonlinear-models produces the following:


At least in these simplistic examples, my suggestions above hold.