Snap selection to x-y component of 3D Cursor just starting off with Blender, and wondering what the easiest way to snap a selection to part of the 3D cursors transform would be.
(TLDR: question below last pic in bold)
For example, if modelling something like a below using a boolean shape to cut out detail, it is probably necessary to align the shape with some existing edges of your model to avoid the boolean function from adding unnecessary geometry.
The below is looking from the xz plane.

Marked here is the corner with the correct xz for an edge, but a different y.


If the 3D Cursor is set to this, and we snap selection to cursor while preserving our offset, we see the xz are correct, but the y component of our selected edge is averaged about the cursor.

TLDR
So the question here is, how would I be able to move this edge to the x,z of either this vertex/the cursor, while ignoring changes to the y component of my selection?
I have looked around online in similar terms for a solution to aligning edges as so, but have struggled to find anything other than manually entering the x,z of the 3D cursor from the world properties (tedious, inefficient), or building the cut out from the point that is going to cause an issue (tedious, prone to breaking with too many points).
I am however a blender noob, so I might be missing something incredibly simple or using the wrong jargon to search. If any of you know of a work around for this, or a better method of aligning edges in general, please advise, as this seems like something that should have a simple solution.
Cheers!
I don't know of a way to snap directly to the 3D cursor itself. Usually you're snapping to a vertex. In your case you can use the preexisting vertex at the 3D cursor's location. Failing that, you can always set your pivot point to 3D cursor, duplicate any existing vertex, and scale it to 0. This will move it to the 3D cursor.
In Blender you can constrain most transformations to either a single axis, or to a plane, including when snapping. If you hit G for move, and then hit Y, you will only be able to move along the y-axis.
In your case, you want to prevent movement along the y-axis, so you would hit G, then SHIFT+Y. This will constrain movement to the x-z plane.
As for the snap tool itself, I usually recommend using the active element setting. This way you have more precise control over what is snapping to the target (the highlighted white vertex, instead of whichever vertex is closer.
Here is how I would solve your problem without even needing the 3D cursor:


Select the vertex that you want to line up to your target edge. This will set it as the active element.

Select the rest of the mesh that you want to move. You can either hit A to select all, or L to select only the contiguous parts of the mesh.

Hit G for move, then SHIFT+Y to constrain movement to the x-z plane.

Move your cursor to the vertex you want to snap to, and click.