I think the pennant is already flying. The Phanatic had it the day they clinched. Someone who actually went to an NLDS could confirm if they noticed it was up already. But you definitely don't have a ceremony for it like the NL pennant. I never noticed the 2023 flag.
The ring everyone got for 2022 is starting to feel faintly ridiculous too. Not to diminish what the 2022 team accomplished, but how do you talk a big game about World Series or bust when finishing second actually did get you an outrageous piece of jewelry, and now it's the only one in three tries?