Oops! I think he blew his turbo

Back in spring I bought my son his first car - 2006 Jetta TDI with just under 280k. Good shape, all the options and ran well, but had sat a while so some things needed attention. So we did brakes, wiper armature, battery and tires. All said and done into it for about $2750. He was doing his first oil change the other night and mistakenly took the oil cooler off thinking it was the filter. He put it back on when he asked me "what the heck" so I (the old out of touch guy) googled it and watched a video. I showed him the error of his ways and he finished the oil change. Unfortunately, I was sick that day and not helping him. He didn't tighten the oil cooler enough and when driven the car was screaming "low oil pressure - shut down engine" after 1/2 mile. Got it home and figured it out - got more oil in. Now we have a P0299 turbocharger and P0131 O2 sensor code. Car has squat for power and smells a little funny. I am thinking he torched the turbo (and potentially caused other damage). He's also coming due for the timing belt. The local VW repair shop (not a dealer) says it's a big project for the turbo, potentially other issues and he recommends replacing at least the water pump with the timing belt. Any input? Would I be better off putting in a different motor w/turbo in case something in the engine got scorched? Junk it? Rather frustrated with my 19 year old who's favorite phrase is "I know Dad!"

Did the car loose all the engine oil?
Depending on.how long it was ran like that and also goving that the low pressure light only works above 2k rpms there are chances extensive damages were made,
Since the oil is pumped from the bottom up, the top end os the first one to suffer.
Cam, caps and followers need to be inspected
Probably turbo is damaged
The oil pan should be removed and the main bearings inspected. I believe reddish color indicates trouble.
Yup. Running the car with no oil is expensive

Running the car with no oil can be expensive. However I would find a good used turbo and install that before I replaced the entire engine. My daughter cracked her oil pan (hairline) on her bug despite the dieselgeek skidplate. The county was doing bridge work and failed to mark a huge cutout they made in the road.

She drove it probably 15 miles and the low oil light came on in the middle of a long bridge with no shoulders. The turbo was shot but the engine has been fine. Ten thousand or so miles and counting.

Doing a turbo is something that you can handle. One tip would be to remove the windshield cowling, I’m going out on a limb here and say it’s probably quite similar to an MK4, that will give you additional room to work when removing the turbo.

^^^^keep in mind a PD has a marginal oiling system for the cam from the factory to begin with. Inspect cam and associated hardware.

Thanks for the input. We are running a scope down to check the cylinders and will take a look at what you all mentioned. Will update at some point...

So everything checked out OK and I finally have the new turbo in and the car running. What a project! Couldn't get at anything, turbo came without the exhaust manifold gasket and I got the runaround for a week from the supplier... Around $700 for everything I needed.