Thanks for the comments, chaps! I really appreciate it. Very useful information and I've noted it all.
To answer a few points and give a bit more detail:
- I haven't cleaned the MAF

but I will. I'll see if I can pull a spark plug (only did them 500ish miles ago). The exhaust tips look ok and the MPG seemed normal.
- No-one checked the fuel system. Not that they told me, anyway.
- Once the car is on on the move, it seems fine.
- I'm sure the battery was disconnected, as I think they put it on charge after I queried it considering the car was sitting there for weeks.
I've also had a response from them today. They say that the car was fine on their extended test drives and idled fine in their workshop. Apparently the engine temperature didn't get much above 90c. No EML or DTC codes.
All sounds quite reassuring when I read this back!
However:
The engine temperature gauge no longer sits dead-centre. Its new normal is 3/4's of the way towards Hot. I know these gauges aren't scientific measurements, but this felt odd because it had never gone beyond the dead-centre/halfway point until now. They told me this was normal

They did replace the oil gauge stepper motor (apparently just the motor was at fault) and maybe they disturbed the engine temperature one. Maybe.
It wasn't slow starting as such, but it grumbled into life. Not a clean start as it used to.
The fuel stench was very real and I'm amazed they'd not mentioned it! My partner commented on it as soon as the car pulled up and before I'd told her about how the car was. I couldn't have the blowers on due to the smell, either.
The heat was also very pronounced, and another thing I'm surprised they'd not noticed. This wasn't ambient temperature as everything else felt normal. But the metal gearstick, and all surrounding trim, were definitely very warm. It felt like something was emanating upwards, hence suspicion of the new cats.
On the idling issue - it's true that it occured later into the drive than before, but I also didn't want to keep testing it on the drive home. I hit traffic, had to slow, and it did exactly as it had done before - started chugging, dropping to 300rpm or so, engine shakes, recovers back up the RPM. I therefore kept the clutch/throttle modulated just in case it stalled. When I got home, it didn't do it

It's seems like an intermittent issue, but even when it's idling normally, it still feels like it's mildly chugging, as if it's misfiring.
Also, when it went back in the second time, I mentioned the cats and aftermarket air filter and they said they could adjust the car's map to suit the basic mods. Not for power, but to optimise it. On collection they said they'd made a few adjustments to the fuel trims. That now makes me wonder why that adjustment was necessary?
The EML light is on for catalyst efficiency bank 1 and 2. This was present before it shat itself and before the new cats. I'll see if I can download Forscan or similar to check in more details (if even available)
Perhaps I should grab some new lambda/02 sensors for when the old exhaust goes on?