The problem you will have is meeting the electric code outlet spacing and installing light switches.
Unless you put in a low voltage control system you cannot fit boxes in the area of the pockets on either room.
Yopu can also run into problems carrying the load above the opening in weight bearing wall.
The header span is twice the opening width, and the beams get tall very quickly.
Add in that the door track must NOT be attached to the weight bearing header (it will sag enough to cause problems) and you may not have room from the top from the top of the opening to the ceiling for the required beam.
The resulting walls are also very flexible and weak, despite the metal wrap on the 1x lumber to try and stiffen them up.

Just did this several times in new bedrooms remodel. Two regular 32" pocket doors and one set of two converging mirror pocket doors as entrance to master bedroom closet.
-My framer said it couldnt be done with 2x4 walls, I ordered Johnson hardware and he complained the whole install but it went in and works just fine.
-My door-glass shop wanted $600 to build the two mirror doors; sooo...I bought two masonite doors for $60. and two mirror glass 1/8" thick for $120. and glued them on and hung them myself.
-The electrician said he couldnt wire it....so I called another electrician and he wired it up no problem
-The drywall guy said the pocket framing was too weak and the wall might flex...It doesn't, and so what if it did?

What I learned:
-Some contractors are set in their ways and others are problem solvers
-When building converging pocket doors, use a single rail instead of two with the convergence kit. The two separate rails with converging plate is not reliable to keep the doors converging properly. To solve the problem of either door sliding too far into the other's space, use stoppers above in the center and guides at the bottoms left and right.

Works great! Looks great! I am not a contractor and have great respect for builders. I'm just saying is all...

I recently put in two sets of converging pocket doors from pre-made kits.

One very important thing to do is make sure the converging openings are totally squared up with each other so that the hung doors meet perfectly. While you may be able to force a fit after the fact, you then have problems with getting any surface hardware to clear the frames. We had to go with a cheaper pull because of maybe a 3/32" too tight a fit on one door.

The flimsy pocket framing was cured by attaching full sheets of OSB before hanging the drywall. (My clients don't expect to feel their walls bend if they happen to lean on them.)

Still, a month later the clients called because one door had come off the track when their four year old yanked it and slammed it into the other door. And we all know how careful four year olds are.

(Personally I hate pocket doors and never put them in unless the client insists. Maybe because one of my childhood homes had sliding closet doors that were forever coming off the track and I was the designated repairman.)

"What I learned:
-Some contractors are set in their ways and others are problem solvers"

Or maybe we have done it enough times to know what the problems are?

"-When building converging pocket doors, use a single rail instead of two with the convergence kit. The two separate rails with converging plate is not reliable to keep the doors converging properly."

What a discovery. Stop the presses.
If you cannot get track long enough the best fix is to use a a single piece in the middle and a section on each end in the pocket to make up the needed length.
This leaves any mismatch in the pocket and it does not show.

"To solve the problem of either door sliding too far into the other's space, use stoppers above in the center and guides at the bottoms left and right."

Or cable the doors together so they both operate at the same time.

"The drywall guy said the pocket framing was too weak and the wall might flex...It doesn't, and so what if it did?"

If the wall flexes the drywall will start to get spider cracks and look bad in a few years.

The 1x lumber used for the pre-frame kits (even when wrapped in steel) is NOT as stiff as a 2x lumber wall.

Depending on the AHJ you may NOT get away with wall switches that are outside the pockets.
If the switches well away from the opening are not acceptable, the only thing you can do in a 2x4 wall is put in some low voltage switching (or you can violate the electric code and use undersized boxes).
The switch is 2 wiring allowances, plus 2 more for the wires, plus another for ground.
That means you need a box with a minimum capacity of 5 #14 wiring allowances, or 10 cubic inches.
The shallowest device box for 5 #14 wires is 2 inches deep.
If you try to go up to a 4 inch square the minimum depth is still 1.25 inches. Closer, but you still need a plaster ring that adds about another 0.5 inches.
Neither of these will fit in a 1x wall since 0.75 inch wood + 0.5 drywall only gets you to 1.25 and you still need a plaster ring for a 4 in square box.

The Johnson track kits cannot come off the track because of the design.
They use 3 wheel (4 on the heavy duty kits) boggy inside a 'C' shaped rail (the opening points down).
There is simply no way to get them 'off the track'.

The biggest problem with the Johnson kits is the plastic guides scratching the face of the doors.
TI solved this by using aluminum angle on the floor of the pocket and a groove in the bottom of the door.
The other 'trick' is to extend the door by about 1.5 inches on the pocket side if required to keep any panels centered when the door is closed.

I have not seen a linkage kit that works well, so I still make them up using 1/16 in aircraft cable and steel pulley wheels designed for sliding doors.
The wheels can be mounted on 1/4 inch bolts and placed as needed so the doors move at the same time.

Are all the things brickeye said still the best way to do this?

brickeyee is still right. (I can't quite wrap my head around the cabling part, but that's not a core detail. Our kits take bumpers in the track to stop the door from overshooting the middle. We use KN Crowder hardware, but they're a Canadian company, so might not be readily available in the US.)

We have a set of double pocket doors in a standard 4'' wall. These are original to the house (vintage 1964). They still work and there is no problem with the wall, either.

I don't know what kind of track system was used, but I do know that it is possible to fit a pocket door in a 4'' wall.