Thanks everyone for the advice.
I ended up using Fuchs Titan Sintofluid 75W80 gearbox oil. This was £40 for 3 litres off eBay, whereas getting the OEM oil from somewhere like darksidedevelopments.co.uk was more like £110 for 3 litres (
https://www.darksidedevelopments.co.uk/products/genuine-vw-transmission-oil-g-052-911-a2.html). I read around the Internet that Fuchs Titan Sintofluid was the same as OEM rebranded. A lot of people just said to stick with OEM, but I couldn't find anywhere that said that Fuchs was bad in any way, so I thought I'd give it a go.
It looked to be about the same consistency. Very thin. I think the oil already in the gearbox might have been slightly thinner, but then again it was hot when it came out so it's not a fair comparison. Either way it didn't look too far off.
The oil that came out of the gearbox was pretty dark, as expected.
I've been driving the car with the new oil for a couple of days now. The gearbox feels absolutely fine. Nothing suggests to me so far that the Fuchs Titan Sintofluid 75W80 was the wrong oil to use. I wouldn't say changing the oil has made a massive difference. Possibly slightly smoother gear changes, but that just might be a bit of a placebo effect. Either way I'm glad I changed it.
It was real easy to change the oil as well -- just a 10mm hex/allen bolt for the fill and another 10mm allen bolt for the drain. I ended up feeding a PCV tube with a funnel attached down through the engine bay to fill up the gearbox with the new oil. About 2.2L came out, and it started to overflow after about 2.4L went in.