The Federation is not rebuilt. Before the Burn, it was over 300 worlds. Now it's just over 60. Being 20% of the size it used to be at its peak, and less than half the size it was during TNG, doesn't make the Federation "rebuilt".
Earth rejoined, but Earth isn't the main focus. They're not going to replace all the standing sets. Starfleet Command will still be where it is now. Rillack is still President. Vance is still Admiral. Discovery will be sent on a different adventure. Earth is not as big of a deal in the 32nd Century. If we even see Earth represented at all, it's going to be through Ndoye, who always has a dissenting opinion. Earth will not have the prominence it once had and it won't be portrayed in as positive of a light as it once was. So, in fact, nothing of substance has changed.
"Earth rejoined the Federation!" is a background detail in Disco World. It's a notch under Rillack's belt. "I got two founding members to rejoin! Remember that when I run for re-election in a few years!"
I'm not like, "Oh! Earth rejoined! Ugh! I'm not interested in the series anymore! Even though Earth's not the main focus! But, honey, look at this! Come over here. Earth rejoined the Federation! I just can't watch this show now."