Pokemon Scarlet & Violet has been available for almost two weeks, will be getting a patch to fix its issues, and its competitive arm is about to be activated. Series One's rules have been outlined, and Pokemon has confirmed neither paradox nor legendary 'mons are eligible.
The rules for series one can be found in Scarlet & Violet's Poke Portal, and Centro Leaks has clarified that the aforementioned groups have been banned from competitive play. Those of you who play competitively will know this isn't out of the ordinary. As highlighted by Serebii's Joe Merrick, it also doesn't mean those Pokemon will be banned from competitive play forever.
While the guidelines in place for series one will remain for the first two seasons which end on January 31, the rules will then change. Paradox Pokemon will likely be introduced to competitive play shortly after that, and legendaries a little deeper into Scarlet & Violet's cycle. Adding them to the mix usually happens a few months in to give seasoned battlers an additional tactical layer to include and prepare for.
Although Scarlet & Violet's paradox Pokemon haven't been officially classified as sub-legendary, their stat totals are pretty comparable. That coupled with the fact they are entirely new to the Pokemon series likely explains why they can't be used in competition for the time being. Other than those two caveats, the only other parameter you'll need to be mindful of when assembling your team is making sure all of your Pokemon are part of the Paldean Pokedex.
Scarlet & Violet's first competitive season begins on December 2 and will run until January 4. If you don't like Pokemon's official parameters, there's unofficial competitive play already underway courtesy of Smogon University. The community of players has already banned four Pokemon from its most popular category, adding Palafin and Iron Bundle to its ban list earlier this week.