Many (most?) ratings these days are self-assessed by the developer/publisher.
The review process has been heavily streamlined through IARC, so you can effectively get ESRB/PEGI/etc simultaneously. Governmental ratings (like GRAC in South Korea) still require you go through the government agency – but some stores like Epic or Oculus can effectively do this for you – and even then it’s still self-assessed.
Some of the storefronts offer help with ratings, in a way doing what a publisher would do, if you self-publish. You take a quiz to determine ratings and ask questions before the rating boards even know you exist.
Ratings boards don’t typically play the game. Sample screenshots and descriptions can be included in some submissions, especially if there’s a grey area or the submitter is inexperienced, but it’s often just apply and get your cert.