It might be simpler to review this game by micro reviewing its "franchise" as a whole first.
Persona 3: Not the first game to mix dating sim time management with RPG, but certainly the defining flashpoint. What I adore about this game is that it has a strong sense of making your party separate characters from you as a player: you cannot give direct commands in combat, if you want to more easily grind in an area you can order them to run around the dungeon on their own and jump into any encounters if they get in trouble, they'll complain that they don't like how the equipment you gave them looks, etc. As an extension of this they're also far more distant from you than the rest of the series- rather than being your friend by default, they're more like co-workers. You can become friends only if you choose to.
The series would immediately move away from these elements because not having control over characters in a difficult turn based RPG is, in fact, a huge pain in the ass. But I also think it's the tip of an unexplored iceberg in games.
It also goes much harder on the time management element- fatigue is an unavoidable status effect that forces the player to take breaks from the dungeon. I actually think this part is rather unfortunate that they moved away from, because it gives the game a much better pacing- later entries instead just make MP recovery the limiting factor that eventually becomes irrelevant as the game goes on and gives you more options, turning the meta of time optimization into just doing every dungeon in one day, which can drag when dungeons are so long (though I have no idea what a perfect run of Persona 3 looks like, maybe it's a miserable exercise in doing dungeons in one day with sick party members so they removed it for the sake of perfectionists).
Later remakes and ports would gradually remove these controversial elements, but as a result I see a lot of first time players wondering why the game was ever a big deal. And they're right to do so, without all the friction and the novelty of innovation all you're left with is a writing formula that the team got dramatically better at.
Persona 4: Summer nostalgia fiction seems to be a bit of a thing in Japan, the most defining one in video games being Boku no Natsuyasumi- a game that is strictly about a boy's one summer vacation and how you decide to spend it. While Persona 4 technically encompasses most of a year, its yellow color scheme, premise of the protagonist having to spend a year with relatives in small town Japan, and pop flavored music evokes summer way too hard for that not to be the intention. It also nails it.
In general it's a stone cold must play classic. The warm vibes you get from the cast of characters are second to none. I was too dumb to solve the murder mystery because my brain could not trust a story with supernatural elements not to introduce new rules out of nowhere, but the game does not actually betray your trust. Thematically it also has some interesting things to say.
Not necessarily flawless in that dungeons are still randomly generated empty corridors that are basically just there for battles to get in your way, but having theming that's relevant to the plot goes a long way. The battle system remains largely about using elemental weaknesses to prevent enemies from actually getting any turns, which can get repetitive in a long game, but it's still short enough at 60 hours that it isn't really a problem.
Persona 5: This game is an interesting case study. On paper it fixes every problem with Persona 4 while vastly increasing the production value. Every dungeon is now hand crafted with gimmicks and other variations. Bosses have more elaborate mechanics. The menus are not only the prettiest, slickest menus ever put in a video game, but they're also insanely snappy letting you button through battles as fast as you want. The plot has the supernatural elements interact more directly with the world than ever before and it's interesting in a way that raises the stakes. The same warmth in the main cast from Persona 4 appears again.
And yet it kind of falls short as a whole. That warmth feels like a hollow imitation of Persona 4 considering the drastically different city setting with the kids going through much harsher things. It also raises the length to 100 hours without actually adding much depth to the combat, so it really wears out its welcome. Perhaps the wait being so long that I beat the previous games after its announcement and still had years to go is part of too high of expectations. But it's kind of the best made yet also most disappointing game.