I sometimes see others walking around 24/7 in these boxy (usually red) headphones that don't seem to connect to anything nor have the capability to play audio from a device. What are they for?

https://www.bunnings.com.au/craftright-ear-muffs_p0401332

Like that? Hearing protection.
I know some people wear them in public to avoid overstimulated.

Earmuffs like these maybe? For people with autism who are sensitive to noise.

could just be plain old ear muffs, for noise reduction.

Like others have said, likely autistic peeps that don't want to get overstimulated; however, could also be that someones turned them into bluetooth headphones with an arduino. Lot's of space in those for electronic shenanigans.

You may be thinking of Ear Defenders. I wear a Bluetooth headset with flanged earbuds as they are more discreet.