what to do where hardibacker meets drywall?
You should have framing backing a seam between wall panels, especially if one of them is going to have tile on it.

The reason is one panel can flex if any load is placed on it (e.g. lean your body against the wall) and with that floating edge, it will be easier to crack grout or tile. It has less support than the center of a board.

I would rip out drywall to the nearest studs then sister those studs. Add horizontal backing as well between the studs, assuming the tile is not going all the way to the ceiling plate. Then attach your cement board: it should have a wooden lip all the way around to attach to, with that wood secured to the studs. That wood you added becomes part of the framing.

That will give a much sturdier backing for your tile.

Note: you can certainly have a floating seam, I have seen some people say that is fine. There are ways to do it. But if you have each seam backed by framing, you will get much better results.

Also, do not forget about vapor barriers and waterproofing if required by local code. Cement is porous and does not stop moisture: something like REDGARD will stop water in its tracks.