I stayed up until 6am reading everything I could find on those 330plus (and 340s).
For less than $200 dollars that will do everything you want to do.
The option I was aware of was a $2,000-$2,500 option depending on how extravagent a screen desired (6.5, 8, and I think 9.2). That's for a complete swap to current MIB2 unit.
The 330 is a VW solution. These are pulls from the Chinese market.
There were early reporting of back up camera issues, etc. because the firmware is being updated by a third party but they seem mostly resolved and don't have any bearing on you anyway...since you don't already have a backup camera when you want one you can buy one that you are reasonably certain to be compatible with the 330.
There are hundred page threads to sift through for info and advice, but I'm going to send an order out this weekend and I'll be able to help you out with any technical information. I've been reading up on this stuff for a good 5 years or more and this is the most straightforward way to achieve what you want. The aftermarket solutions are going to be spendy and sub-optimal. Everything, and I mean everything, runs through that unit in the VW. It will take time and/or money thrown at an aftermarket unit to get it and the vehicle back to somewhat stock+ functionality. There's a reason people don't do this frequently even for those of us with some experience under the belt.
I believe this is the most up-to-date model for your application: 6RF035187E
and looks like this:
You can see the Carplay feature in the picture. It simply mirrors your phone. You lose HD Radio and Sirius compatibility (a feature imo), but none of that matters if you can use pandora or spotify or iheartradio, etc., waze/maps (no more worrying about nav updates) all navigated via touchscreen on your center console. I would not add any vehicles to Sirius and in fact would suggest dumping the service (unless you have lifetime or your wife demands it). Our household has the family plan, which I think is about $60/yr for 5 accounts unlimited streaming, local downloads if necessary, higher quality. I haven't listened to the radio in a good 5+ years except the occasional 91X but isn't the same as it was twenty years ago.
After driving our 2016 Golf for three years with Carplay going back to the crappy MDI system that we have was my only hesitation in getting back into a TDI. I budgeted a couple grand for an upgrade and bought low enough I wouldn't be hurting too badly. I'm still hesitant to go full out upgrade because more features are coming down the pipe, which are unlikely to be updated into older units. Features like BT Carplay will be noticeable quality of life updates so I'm holding off on spending $2K+. Unless I'm mistaken, when this was first an option the cost was quite a bit more and still a trailblazing adventure even with the hefty price tag.
For $200, this is a no brainer.