Calling the main character The Phantom for convenience's sake.
Thanks to Ridley, Artsi, Feonix, Duckroll, and Stone Ocean for the corrections/additional observations!
Shot of a helicopter approaching a city
Shots of what's seemingly a casino. Two figures in the crowd are clearly running, possibly aware of The Phantom. The scene transitions to close-ups of security.
The phantom himself, sporting a white mask with jagged black eye marks
The casino is seemingly very ornate
Now the opening. First a shot of The Phantom
Followed by his teammate, Anzu Takama, her body suspended by some red cable
Another masked individual is sitting on the signboard. Presumably fox-themed?
The Phantom's third revealed teammate, Ryuji Sakamoto
First shot of the new velvet siblings. A pattern of black bars constantly changes in front of them, but they overwhelmingly appear as jail bars
Something seems to be up with their eyes facing away from the viewer. Also, while it's hard to determine their sex, the one on the left has a ponytail.
The Phantom descends onto the city, creating an explosion which eventually shoots out a winged figure seemingly wearing a top hat (and possibly mask?) with a giant black chain chasing it and latching to its neck. This could be The Phantom's persona, as shown by
the poster handed out following Persona Superlive.
The Phantom riding in the train. Unlike his masked persona, he's seemingly much more docile. Note that the calendar system in full effect, and that NPCs appear faceless. This could be a technical limitation leveraged for symbolism.
Train station. Notice the gaggle of businessmen slouching and generally looking depressed.
And the classroom. Note the green clover on An's hoodie. The Phantom gets chalk thrown at him for dozing off by his teacher.
Some scenes seemingly involve cut-ins of the character's faces
A black cat next to An?
Another cut-in
Seemingly their base of operations - what looks like a coffee shop. There's a mascot-style cat with them named Morganna, meaning that the normal world and whatever its alternative are can interact
Pretty slick transitions
Ryuji seems like a goof, sliding down the rail playing air guitar while wearing a "ZOMG!" shirt
Anzu seems to be a graceful ballerina, but for some reason, the clover on her hoodie is now red.
A seemingly normal black cat transforms into Morganna. The names across the screen are the Latin words for the seven deadly sins, as well as two more words. Luxuria is lust, Acedia is sloth, Cavum is hollow, Avaritia is greed, Gula is gluttony, Ira is wrath, Invidia is envy, Irritum is void (ueslessness?), and Superbia is pride.
The image cascades to an array of screens. Note the loading bar at the bottom. The internet might be a big part. The name on the bottom icon is Superbia.
The pause screen. It seems to be paused at the first dungeon. Note that social links (commu) aren't there. Also note that there's a party command, meaning there are probably more party members.
Equipment. The Phantom seems to be able to equip both knives and guns, but on top of that, he can also equip armor and clothing separately.
A look at the possible knives. The transition involves him flicking a bullet to the right.
A train driver, seemingly possessed by something. Whatever it is, it causes him to crash his train. A police officer might there on the scene, so the affliction probably didn't hit right before the crash.
Whenever the phantom falls, he leaves a strange red circle around him. He's also alone here, possibly as part of the tutorial?
Whatever he's infiltrating has suits of armor walking around.
Shots of him jumping across chandeliers.
Persona 5 seemingly implements a cover/sneaking system, which lets him cross short distances without being noticed. He also seems to contort into some black shadow as part of the process.
Some sort of lab/clinic. I can't read Japanese, but it seems her name is Tae Takemi, who offers drugs/medication.
Ryuji seems to get on An's nerves, while The Phantom is pretty nonplussed.
Something bad happens during an operation, though it's hard to tell if it's played for laughs or is serious.
The weapon shop, courtesy of on Iwai Munehisa. A lizard/gecko diamond pattern grows across the screen underneath the fence.
Individual party members. The Phantom has both "Joker" and "The Fool" underneath his name.
The velvet room - a jail cell. The Phantom seems somewhat deranged and/or unhappy about his situation. Note the giant chains.
Combat. The Phantom wields a small handgun. During the currently-active party member's turn, their icon changes to them holding their arrest board.
Shadows are gone in favor of demons again. Ryuji is also shown wielding a shotgun, while Morganna wields a giant slingshot. Though it's not pictured, Anzu also uses a submachine gun. It seems that the party can also attack with their firearms in unison.
An's suit. She's shown wielding a whip. It appears that certain attacks make the screen go grayscale and slow-motion.
Ryuji is shown wielding a pipe.
And Morganna is shown with a cutlass.
The new all-out attack. It involves them going black and quickly dashing around the screen. Considering the sneaking animation, it's unknown if this is just stylistic or something else.
Next scenes of the three humans skating across a freeway without anything on their feet. Ryuji is shown swinging Morganna around, before throwing him at the signboard. However, when the cat hits it, she turns into a black shadow.
A closeup of The Phantom, the top half of his face covered in blood in the shape of a masquerade mask. The scene shows him starting to use his persona - blue flames start rising from below him while the blood dissolves. For a quick moment, the flames turn into another mask before consuming his face and slowly spreading across his body.