If you're hearing the audio left or right and on earbuds or headphones, it's because the audio announcements are in different locations in the game

This video shows all Eggman's PA announcements in Sonic Colors: Ultimate

Timestamps
0:00 Intro
0:09 Tropical Resort
2:55 Sweet Mountain
4:08 Starlight Carnival
5:55 Planet Wisp
6:06 Aquarium Park
7:38 Asteroid Coaster
9:09 Terminal Velocity
9:23 Game Land
9:33 Egg Shuttle
9:44 Options Satellite
9:55 Outro

Sonic Colors: Ultimate available for Xbox Series X/S, Xbox One, Nintendo Switch, PS4, PS5 & PC