Just a heads up you should avoid spraying any grease/oil/lubricants on the belt as this will cause even more slippage and can swell the rubber, which will eventually destroy the belts.
The correct way to do this test is by spraying water with a spray bottle or rubbing bar soap on the side and grooved part of the belt. If the squeal quiets then it's likely the belt. Although that's not to say there could still be an issue with the drive belt components (pulleys/tensioners).
If I were in your position I would replace both belts (accessory and supercharger) with quality replacements (genuine audi/continental/gates) from rockauto or fcpeuro. Then, while they are both off, inspect your tensioners and pulleys for and in-and-out play or wobbling. Also, spin them by hand and listen for any noise.
A good pulley will have ZERO noise (or very close to it), and have absolutely ZERO play. Some idler pulleys will have the tiniest bit of play even when new though.
To change these it will be easiest to put the car in service position if you know how to do it, although it can be done without, it will just be much more difficult and annoying, and you'll probably need certain tools.
There are a few good videos on youtube, start there first.
I haven't done it myself yet, but it's likely that the hardest part of this job is putting it in service position (which isn't very hard).
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