Replacing old tile kitchen with wall
The backer board is usually screwed to the studs , just like the Sheetrock although some used to use nails back in the 70’s.  The problem with demolition on this side of the wall is it can cause issues on the other side. The shower should have a vapor barrier moisture would not be my concern, but if any hammering is done on the wall make sure to get a grout &amp; Tile sealer and reseal the shower so it will not have a leak.
I like to work with fresh Sheetrock to have clean straight walls it may be easier to Remove the cabinets they look to be sectional. Remove the backer and install fresh Sheetrock,
another option is to overlay Sheetrock on top but that is hard to hide the edges  with cabinets in place but I have done it with 1/4” where I wanted to cover a large mess without all the removal, then extending the receptacle  and switch boxes with extenders is simple. The tough part is very precise cuts on the Sheetrock to slip it in place, but this may give you the clean straight wall look you want with the least work.