I don't pick my nose or fart in public. I don't lick a plate or use the finger to scoop what's on it if I'm in company. I also don't phase out and daydream half as much in public, an exception would be on public transport as everyone is kind of gazing at nothing so it's not obvious I'm in another dimension entirely.
As for other things, no, I don't have that kind of filter. I will occasionally stop and stare at that interesting pattern on a tile or leaf, follow closely with attention what the birds are doing, sniff if I sense an animal and see if I can find its trail (possums and rats usually) etc. I still build sandcastles at the beach and if the opportunity arises I'll scribble on cardboard coasters or paper napkins.
It's easier to switch off my senses if I already know my surroundings. Also people who caught me daydreaming teased me afterwards about it, apparently my thousand yard stare and overall unresponsiveness it's either concerning or hilarious to people.
That's annoying! I always assume someone is just deep in thought but I don't know why I'd give someone shit for thinking.
Reminds me of people who like to say "its not that deep" all the time in response to questions that are meant to spark conversation. Like some people take pride in not using their brains or something.
Eh, no biggie! People do that when they don't experience a similar behaviour themselves.
As for the not that deep crowd, I always thought they're either self conscious or fear touching a triggering topic. Refusing to engage means they won't be judged on their opinions or ability to reason and express themselves. Trying to pass a cool is what gives away they're trying to cover up something.
I think part of it is them being self conscious but I think it was also just seen as a "cool" way to behave like you said. I often saw this mentality on reddit of course and in various discord servers where people just couldn't back up what they were saying - so someone else approaching them with an in depth take, just causes them to try and shut things down with "oh its not that deep".
Like its a very dismissive phrase meant to shut down conversation.