Okay.
Final decision of whether the player in Splatoon 3 is Agent 5 or 9, if they join the NSS in the first place. The distinguishing factor is whether Pearl, Marina, and Sheldon are Agents. All three character aid the heroes on their journeys. Sheldon creates special weapons just for Four to use on their missions, and Pearl and Marina use hacking, theft (no seriously), and other techniques to help Eight escape the Metro. However, they don't seem to have the same role as Three, Four, and Eight. When they appear in Octo Valley, Callie and Marie have a similar guilding figure kind of role (Three being the person they guide), but it's revealed that Three's uniform used to be worn by Marie, Four's by Callie, hinting that they had similar adventure before the events of the game. Another character to observe is Cuttlefish, who isn't an Agent but is still part of the Splatoon, proving that someone can be part of it without being an Agent, which leads me to my final conclusion.
Pearl, Marina, and Sheldon are not Agents. They are likely part of the New Squidbeak Splatoon with their own roles (lethal voice, team hacker, and weapon supplier maybe?). Agents are specifically characters who go on missions or have been on them some time in the past, those being Callie, Marie, Three, Four, and Eight (Eight is a little more confusing, as they don't fight Octarians for the same reason the others do, but they're the only one doing any challenges in Octo Expansion, and traveling to the Promised Land is just as much an adventure as saving the Great Zapfish). If the player in Splatoon 3 joins the NSS, they'll almost positively be Agent 5.