Owning your own home

Would the plan be to remove the existing render?

Yes - the acrylic render is just about the worst possible thing for a solid wall building. It fails (without fail), prevents drying out, and allows damp to penetrate.

Is the new external insulation breathable?

It isn't. However, in theory at least, it moves the dew point further out of the building, and removes any cold bridging problems.

If the render on top of it fails, it is also easier to repair & less damaging to the substrate.

Again - in theory.

Ideally, I'd like to lime render properly, but that is just as expensive, harder to find trades with the actual experience. And we'd still have an insulation / cold bridging / condensation problem.