Installing a pocket door in an arched opening can be anything form impossible to just harder.

You need to be able to remove the door, and the non-pocket side of the arch often interferes.

Using a pair of pocket doors that move together is one way to make it work.
Each door is only half the opening in width and with a carefully chosen arch style each can be removed.

Another alternative is to use trim to create the arch, but mount it using screws so it can be removed on one side.

One side of the header trim on any pocket door normally needs to be removable anyway.
It is possible to use concelaed mounting o that nothing shows on the removable piece.
I have cut dovetail shaped recesses in the header trim strip[, and put plastic details on the actual header so that nothing shows.
Even 'picture hanging' type recesses can be made to work.

The strip slides towards the other side of the header (blocking the door) and comes down when the door needs to be removed.

Remember not to seal it in place with paint.

Thanks Brickeye. I will be creating a new opening, so there is no door in that space to currently remove. I guess you mean that the new door would need to be removable? I would like double doors.

Not sure exactly how to tell my GC to build it. Like you said "use trim to create the arch..." but how?

What about a barn door? They make a lot that are very elegant that are easier to maintain etc.

Archie123 - I did consider a barn door, but one of my main purposes is to keep my dog confined to kitchen while we are not home. Not sure if a door that is only top mounted would suffice.

Also, I would not have clearance to move the door to the side unless it was a pocket door. I was thinking a pocketdoor could slide into a narrow pocket built into a new half bath wall.

I think in an application like this a bottom-wheel arrangement would be better. I have no idea if anyone still makes them, but I have worked on old houses that had the trolley wheels mounted in recesses in the bottom of the door which rode on a single brass rail. The rail was round-topped and the wheel had a matching concavity in it's tread.
The top of your door could then be cut to the rounded arch shape, and to remove it, you would need to envelope the jambs with a 1/2" thick removable stop molding. You could thn lift the bottom of the door clear of the rail and slide it out, the top pin slips from its slot at some point.
One nice thing about the bottom rail sliders is that they fit very close at the floor line and effectively can seal the room from air, light, and sound. The downside is the brass bottom rail is not comfortable to step upon; it's like the rail for sliding door screen panels, BTW.
Casey

"I guess you mean that the new door would need to be removable? I would like double doors."

Pocket doors that are permanently trapped are a real problem.
While new Johnson hardware is very good, there is always the possibility of something breaking.
Not being able to remove the door completely makes a repair job major work.

"Not sure exactly how to tell my GC to build it. Like you said "use trim to create the arch..." but how?"

You use applied trim to arch a square opening.
Any good trim carpenter should be able to figure out how to do it.

The floor mounted 'track' type systems have pretty much disappeared in favor of the hanging systems.
The track systems worked reasonably well, but the track was always a tripping hazard (even when fully recessed).

'Double acting' (both doors move together in unison) is not hard to do, and kits are around now.
The older method was to install metal sheaves (sliding door sheaves work well) bolted inside the track to the top, then thin aircraft type woven cable (1/16 inch) was installed in a loop the length of the track on the sheaves.
Metal tabs on the top of the door than attached to the cable to make both doors move together.

It makes a very elegant door.
It is rather stunning on wide opening.