Yes removing tile without breaking them is an art and honestly more time consuming than using a multi-tool to cut around the entire area, and then pry the entire tile surface up via the cut out subfloor as a single piece, then use a plywood the same size as the offset and glue the old subfloor to the new riser plywood.

If the subfloor is concrete you will have to remove them, you might want to see if you can find matching tiles to replace any that get damaged, or consider what you would like to install in the event that they do get damaged.

First thing I would do is pop those framing pieces and see what I am working with below the tile.