Shop vacs tend toward noisy — the Fein Turbo, and a couple of the nicer Ridgid vacs are supposed to be reasonably quiet — I gave up and Drank the green Koolaid
I don’t like the idea of using a compressor — it just blows dust around, moving the problem to somewhere else and potentially increasing what’s airborne and breathed in.
Side panels are decorative — the machine actually rests on the front/back edges — lots of photos of the machine running without them (don’t do that) but it’s okay to remove them and replace them in an enclosure (a number of folks have done that)
I put my machine on a Yoga mat, and the table on carpet with some extra carpet pads beneath the table legs — if there had been more of the appliance isolator bumpers in stock locally, I’d’ve bought them (got one for the new washer).
The community has tried to collect links at: https://www.shapeoko.com/wiki/index.php/Soundproofing_Enclosures