Mike,
If it were me, I would apply new sheetrock and then the ¼ inch hardiboard to bring the area back to the same plane as the existing wall. I say this for several reasons. It would allow you to treat the seam between old and new with sheet rock mud and tape (I would use the mesh tape to tie to the Hardiboard) and it will bring the tile out far enough to stand proud of the counter top and sink back splash. That is an area that is susceptible to water/spills and you don’t want it going behind the cabinets. If the tile is more or less sitting on top of the counter, a bead of silicon chalk will make a good seal. I would be afraid that keeping the new tile surface and substrata flush to the existing wall would create a situation where you have two dissimilar materials butted against each other and they will expand and contract at different rates as the seasons change. This could mean that the seam between old and new and where the tile tucks behind the counter will open up in the winter (when the house is drier) creating a crack.
Looking at your photo brings up a question. Are you going to run the tile up along the cabinet on the left? It looks like you will have to add some wood to support whatever substrate you apply.
It looks like you will have the window trim and the cabinet bottom to kill the tile to on most of the run. I would lay out my tile so that the cut edges are there. That would save a bunch of nosed tile and is how it is normally done. I would also start with a full tile against a nosed trim piece on the left side and work to the sink. Now there could be an exception to the last sentence as the tiles layout to the sink. Your hardest cut will be around the sink edge. You do not want a small skinny edge right there. It will be to hard to cut. If it does work out that way, leave your cut edge next to the nose trim and have a full tile next to the sink. When you cut your tile to fit under the cabinet and window leave enough of a gap for a chalk bead. Same as above, two dissimilar materials will expand and contract at different rates.
Hope I made some sense here. By the way, aren’t those Bose radios great.
MarkV