I know that competitive battling has a different strategy than regular battling for in game, because you rely on status moves more, but I have never battled in the Battle Maison before and I need to know if it is competitive battling or not.
Yes, the Battle Maison is Competitive Battling, albeit in-game Competitive. This is mostly due to the Flat Level (All set to 50 unless below it), need to have items, etc. Keep in mind that the Super Format is more Competitive than the non-Super ones (They usually use non-fully evolved Pokémon).
Source: https://www.smogon.com/forums/threads/mastering-the-maison-a-comprehensive-guide-to-the-kalos-battle-maison.3502496/#:~:text=What - The Battle Maison in Pokemon X,very engaging, challenge for many competitively minded players.