for reliable shield cable repairs in aviation they show that you need another segment of braid that you put over the junction and then put two lap joints around it or for temperature reasons I think they also use constant force spring tape to join the new segment of braid with the two other segments if you can't solder it, but usually its teflon wire there so its OK to solder over that.
but that is just shielding telemetry from noise. I would imagine you could do a coaxial splice like that, but then you would need to put some heavy duty heat shrink on it that can clamp the braid down to the original diameter and tightness if it was heated very uniformly. The solder is going to show up as a discontinuity.
If you wanted it like really good I think you would have to splice the braids together using a laser welder wire by wire with one hell of a cable fixturing aparatus to get it all together. But it also would involve super precision cutting and fitting of new dielectric (unruly plastic) with minimum gap, and I don't know how you could keep the middle conductor, which is often load bearing (steel) spliced to its original diameter. Again, I think you would need laser welding for high frequencies, followed by having to sand it flush, and replate it with silver to get it anywhere near original strength with the same diameter.
Since its only a few thousand strands in the shield, maybe you can weave them in place over the wire in the same pattern as the cable with some kind of laser welding robot... that way you would have no interface really other then a bunch of really small welds. Or you could fusion splice them mechanically (cold weld machine).
Yeah actually to get the middle conductor the same and equally strong you would need to cold weld it with a 50 pound small diameter wire cold welding pressure machine.
Maybe they would do this if they had to fix an antenna wire on a modern armored air defense frigate or something, if it saves having to cut and patch 20 steel armor walls to run a new wire
And even if you do all the correct wire fusion techniques, you are still left with the dielectric which has a slit in it so it can be fit over a joined cable. Its going to be a problem if the wire moves at all ever. To get rid of that you would need some kind of dielectric splicing machine extruder thing that can weld the dielectric together
I think this is the only machine that can repair your center conductor to the correct tensile strength and dimensions.
The braid and dielectric is left up to your imagination. Braid seems doable and less critical. Dielectric... you need a plastics guy, or magic glue. I think pretty much all glue would be shit but who knows. Maybe you could 3d print a extension in there that is fused to the original if you find the right filament and put the print head on a complex robotic arm?
then it might be close to the original cable...