Talking about my yumeship because I have nothing better to do and it's almost all angst and also midnight sorry for inconsistency
Murdoc and Sylvester had a bunch of bands together that all winded up failing. Sylvester played bass for them. (Partially canon because of all of Murdoc's failed bands.)
Eventually, Sylvester found out that Murdoc hit and almost killed a guy (2d) in an attempt to form a new band and decided to leave "for good."
Five years later mid Demon Days, the band is discussing potential collaboration to have for a few of the tracks and one of them mentions Murdoc having a friend he used to talk about whom he did music with. Originally, Murdoc hates the idea of going back to Sylvester for help with music but eventually called him up. After an argument over the phone Sylvester eventually agreed to come to Kong for the album.
Him and Murdoc started living together in the Winniebago which they previously shared; evidence being Sylvester's scattered things around the room. (Things like his nail polish, hair dye bottles, lense wipes and miscalanious clothing items.) From the start they hated the living situation but eventually got used to it.
Ok now lore for each album go
Self Titled: During the self titled album Sylvester wasn't in the band but that doesn't mean he could escape it. With the bands growing popularity, he was reminded so much of Murdoc. (Obviously) Honestly he was proud of his old friend for actually kicking off a band but at the same time incredibly jealous. Starting a hand together was their thing and now Murdoc actually got traction from it without Sylvester.
Plastic Beach: Murdoc thinks they should stay on plastic beach, safe from the pirates and all. Sylvester, on the other hand, thinks it'd be better to look for Russel and Noodle. He tries to escape Plastic Beach numerous times but always gets dragged back by Murdoc. When in the time where he wasn't trying to put the band back together, he was listening to Murdoc talk his ear off all day. They did have fun together for the first time in a million years on the plastic lump.
Humanz: Probably the longest time spent together where they actually get along. I can't think of much lore for this phase but overall their relationship is very stable
The Now Now: (I'm aware this album is 2doc centered but I am not the biggest fan of that ship[I'm not an anti I just am not fond of it]) While Murdoc is in prison Sylvester falls into quite possibly the worst depression of his life. He literally can't do anything but write. They write to each other constantly, Sylvester updating Murdoc about the band and Murdoc complaining about prison food.
Song machine barely has any lore I'm also skipping it
Cracker island: they start a fucking cult what else do you want.