I feel like Picard is probably not the best way to look at canon from DS9-onwards. Especially with the whole "the entirety of a scientific, exploration, policing, military, peacekeeping, and survey fleet that spans a huge chunk of the galaxy all gets together in one place for a single day despite the impossibility on every level of something like that, let alone the utter absence of intelligence put into such an idea" thing.
...and then having a galaxy-wide "element blows up" event because some kid had some trauma thing wrecking the entire Federation and having humanity leave the organization it founded...yeah, Star Trek canon kind of went downhill after DS9.
oh god you're making me defend DIS S3 and PIC S3.
... Federation Day is really silly. But it makes some sense. Demonstration Grand Fleets are a thing. As depicted in Trek, it's a surprisingly small Navy outside war time. (My issues with it are too spoilery to get into here.)
So. The Burn is really dumb. But I can see Earth leaving the Federation. Humanity is full of examples of people not persisting in things even when it makes sense to. It also seems like by this time the Federation is no longer HQ'd on Earth, which helps.
Like I don't like either element, and the Burn is what broke me on DIS, but the on-effects make some kind of sense.
That said, both are canon. So.