Mikel,
this happens is if Openstreetmap is not showing the onground facts.
Of course the western wall is under Israeli control, so does most of the westbank.
This is not political correct but a on ground fact.
I would also like to hear your suggestion how to solve this issue.
Don’t get me wrong but it is somehow ironic if the person that caused the removement of Jerusalem from Israel is starting a discussion why the western wall is not shown in the search as a Israeli part.