Fix private properties appearing in custom class doc Property Descriptions

[Cykyrios]

This fixes one of the issues mentioned in #67704, namely private properties appearing in Property Descriptions.
I just copy-pasted this from the part of the code that updates the Properties list, which does work, but it might be a better idea to filter properties in the same way methods are filtered in _update_method_descriptions.

Bugsquad edit:

• Fixes [4.0] GDScript underscored variables in custom classes appears in generated documentation #72705

[akien-mga]

Thanks!