I am aware that URLs pointing to iD can have parameters to load iD in a certain way, ie to use a particular basemap. For example, to open South Africa CD:NGI Aerial, one can just click on:
Nice. What I don’t get is why your URL seemingly redirects to https://www.openstreetmap.org/edit?editor=id#map=19/40.715264/-73.937270. I would expect &photo_overlay=streetside to be preserved in the URL, but it isn’t, so I’m missing some part of the picture.
The corresponding parameters (the part starting with #, called fragment identifier) are not sent to the server. The fragment identifier is read out via JavaScript (location.hash).