These are the songs (from what I can tell) that the game launched with:
Each group got 3 cover songs, while the Vocaloids got 6 songs to themselves, with only one (alive) not featuring Miku at all.
Some groups had covers on launch with Vocaloids that hadn't yet appeared in their Sekai. These are MORE MORE JUMP! (with MEIKO), Vivid BAD SQUAD (with KAITO, and maybe Rin if you count her, but we'll come back to that), and Wonderlands X Showtime (with Rin and Len). The weirdest part to me is that while some of the groups sang with Vocaloids they didn't know yet, most of them didn't have a cover with their second main Vocaloid. Vivid BAD SQAUD are the only ones that sang with their main Vocaloid that wasn't Miku (Len in this case).
Vivid BAD SQUAD launched with either 3 or 4 Vocaloids already in their Sekai (depending how you define in the Sekai), more than the other groups, having Miku, MEIKO, Len, and Rin. Rin is kind of a weird case though. She doesn't appear in the main story at all, but is mentioned, and she appears in the Vocaloid stories for the Street Sekai, as well as having her deafult VBS outfit in the game. I honestly have no idea why they decided to put Rin in there, but Len is likely because he wouldn't have had an initial group otherwise, since Nightcord only had Miku.
The collaboration with Evillious Chronicles, a fairly popular Vocaloid based multimedia project (it's what Daughter of Evil and Servant of Evil are from), is the most extensive to date. Unlike things like the Kagerou Project or Ado collabs, which only had a few cover songs added, EC got several limited cards (one for each Vocaloid, representing a major character they play) and a whole new Sekai to see these characters in. The dialog in this Sekai and the card's side stories all were very well researched, making references to things that don't even come up in the songs. It even recently got a rerun of not just the gacha, but basically the whole event.
The character's featured come specifically from the 7 Deadly Sins arc/subseries, with each being one of the charcters that made a contract with a demon (other than Allen, Len's character, but it's kinda hard to do the Vanity stuff without him). The only contractors to not appear are Sateriasis Venomania (the Lust contractor) and Nemesis Sudou (the Wrath contractor), who likely only got left out because their Vocaloids (Gackpo and GUMI respectively) aren't characters in PJSK.
If you don't know who goes with what sin + their names and songs:
The song that was commissioned for the event, Waltz of the Deceased, even reflects how the event worked a little, detailing the various characters coming together and dancing after all their stories have ended, similar to them all showing up in this special Sekai.
On the official PJSK Youtube channel, there is a short series of audio dramas called the Vivid BAD SQUAD Archives. Unfortunately, I can't find a translation of the dialog, but the more interesting thing is that these feature brand new covers. These are Night Sky Patrol of Tomorrow (with An and Kohane), Dramaturgy (with Akito and Toya), GimmeXGimme (with An and Akito), junky nighttown orchestra (with Kohane and Toya), and TOKIO FUNKA (with Akito and Toya). I need to double check for sure still, but I'm also pretty sure GimmexGimme and junky nighttown orchestra are the only time we see VBS duets that aren't either An and Kohane or Akito and Toya. These covers are not available in-game.
Update 6-23-23: These are still being made! They just announced the 6th one, which will have Butterfly On Your Right Shoulder with An and Kohane.
Ok, so I don't have a lot of info on these as theres no translations for any of it (it doesn't even seem to be on the wiki) but I just think it's neat.
There are these videos on the PJSK Youtube that are, from what I can tell, the calls between the Nightcord members while they are working on songs. Here's the playlist. They are all 8 hours long, but there's not things happening the whole time. People pop in and out of the call to talk. Might be nice background noise, and if there were translations for it it might be cool to see more character moments.
Nomad has 3 different jackets shown in game. The Miku version's jacket was added later.