I'm really thinking that this officially "empty" hospital building, was indeed filled with IDF soldiers during the Iran War, and that they were sheltered there because Israel assumed Iran would not target a hospital.

Remember that the IDF moved their headquarters to underneath the hospital in Tel Aviv.
And all the IDF bases around the country were assumed to be targets by the IDF, so all the soldiers were removed from the bases during the war.
So where were the IDF soldiers sent to, to avoid missile fire? Probably in hospitals like this one, along with elementary school gyms like in Ukraine.