It is a must-play game for all true Japanophile weebcels, as a simulation of Tokyo life it's the best game to ever do it. Excellent story and characters that goes far deeper than you'd think. The dungeons and dungeon-crawling is also excellent, but if you don't care for the story you'll have a tough time enjoying that since the game is pretty much 70% story or more depending on how you play it. It is definitely not a game for everyone, even people who enjoy other JRPGs, but it is an undisputed classic for a lot of people at this point for sure. I would recommend giving it a shot.
I will say that if you only want the story the "Persona 5: The Animation" anime adaptation is actually pretty good in my opinion. It won't give you all the details since that anime is around 10 hours long meanwhile the original game(s) are upwards of 150 hours long, but it will give you all the most important bits and it is a satisfying watch on its own. I'm sure many Persona 5 fans would consider this recommendation of mine blasphemous though, so that is also something to keep in mind. It is also an adaptation of the original Persona 5 game rather than the expanded Persona 5 Royal, but I don't mind that personally, because I am among the few who actually preferred the original, more focused version of the story than Royal's significantly expanded version. Royal isn't in any way bad though, and it is what you should play if you choose to play the game for the first time, otherwise you will be left out of the conversation because when most people discuss Persona 5 these days they discuss the Royal version.