I would imagine these services are less needed on wknds, if that's OP's only availability for gigs. Though I recognize lawyers work gross hours...

I did this for several years before covid. Typically if there was a vendor you liked, you could just show up and ask them about openings, if they didn't actively have signs posted for help. More will probably be looking for help in a few months, since many run a slower schedule or are off completely during winter. Check the vendor lists of market websites to see what looks interesting (do you want to do veggies? dairy? pre-made foods? etc) and reach out to them on social if they're off season.

In my experience the cash thing is rarer than it used to be 5+ years ago. I'm sure there are many vendors that still pay cash, but mine really formalized their business during the time I worked with them and everything was payroll/automated official by the time I stopped (for other reasons, day job became too much to also have a heavy side gig).

It was a great way to get to know a neighborhood and feel connected to the community. I made some great friends. And it was such a change from my desk job to do something physical and outdoors and learn about a completely different industry that was very mentally healthy for me. I may have left DC if I hadn't found this. I found it great for reasons beyond just extra pay.

I wouldn't describe a regional weekend trip that's $500 as 'budget', even if it's NYC. If I'm taking the bus and sleeping in a hostel I'd better be out less than 500 for it.

Though granted it's been awhile since I've tried a trip like that and maybe prices are such that 500 is the absolute floor. Which is sad, if so, and helps explain why many people might never have done what sounds to others like a no-brainer trip.

I've literally shown up to things in leggings and carrying groceries. I've also gone not quite ball gown but like fancy wedding level. And I have shown up in costume. There's no official dress code there (at least, there never has been for any show I've attended) and no one will care what you're wearing. Dress up if you like, dress down if you like! If you just want to fit in, agree with other posters that middle ground of business/business casual is the norm, especially for a musical.