It loops back around at the top. It’s why there’s an eccentric rich person trope and why it’s called “fuck you” money.
If you’re totally financially independent you’re more free to do what you want, independent of class behavior expectations (or even in contradiction of them). They no longer matter that much (unless you’re doing something that requires politics or people).
You're right, everyone is doing that to some degree at some point through out their life. But consider that there exists people who feel they need to dress better just to get the basic respect they deserve. In the case where someone cannot afford the appropriate clothing, it ostensibly seems they are unable to show the respect you speak of and are deemed "less than" because of that, but really their minds and character is the same regardless of clothing. Being privileged is having the agency to pay for the kinds of clothes that impress people and causes them to respect you, and in some cases, without having much other than a nice suit to justify such respect.
You say that like everyone else isn't doing the exact same thing. Being privileged is all about playing the "get everyone else's approval" game. But coming from a different social context it's even more basically a way of showing others respect and earning their trust, so it's not without consequence.