I think the writers just kinda forgot. A lot of the people who worked on the og game don't work with Solmare anymore so we have new writers that have different ideas with the characters / didnt bother to research the original stuff their new work is based off of. There's a lot of inconsistencies between games / series.
Idk all the characters have been flanderized to an extent, and the writers shit the bed with Lucifer and Belphie's dynamic. Belphie is supposed to still be super close to Lucifer in Nightbringer bc if he hated Lucifer, he wouldn't have fallen from the C.R with him to begin with. The writers forgot that Belphie hating Lucifer is recent
Belphie hated Lucifer for the following reasons:
-Spending all his time working with Diavolo instead of hanging out with him and the other brothers. Belphie felt neglected and forgotten. ESPECIALLY since in the nightbringer timeline it's been a year or less since Lilith died and the war happened. Belphie and the other brothers desperately need comfort from Lucifer to cope with their grief but instead they're being left to deal with it on their own
-Voting in favor of letting humans attend RAD because Belphie was blaming the humans for Lilith's death. This was seen as Lucifer being a traitor
-Locking him in the attic
-Lying to the other brothers about where he was
-Not telling the others that Lilith was reincarnated and lived a happy human life Belphie and Beel spent CENTURIES blaming themselves for her death and believing she was suffering and in pain in the afterlife, when really she was ALIVE
None of these things have happened in the current nightbringer timeline. Lucifer has only just now started to neglect his brothers in favor of working for Diavolo. RAD was literally just made and they don't open the human exchange program for another couple hundred years.
Right now we should see Belphie being super nice to Lucifer and trying to spend time with him only to be shut down bc Lucifer is busy with other things. They should depict Belphie going from accepting and understanding that Lucifer has new responsibilities, then shifting to sadness, then anger.
I think this would be good fuel for Belphie and Satan's relationship.
My headcanon on how Satan and Belphie's relationship SHOULD HAVE BEEN:
It starts as Belphie trying to treat Satan as a replacement Lucifer because he needs Lucifer's reassurance to deal with his grief, but Lucifer is busy. Then Satan lashes out when he realizes that Belphie is just using him as a Lucifer 2.0. Then Belphie realizes his mistake and finally sees Satan as a new person and not a clone. THEN Belphie realizes how Lucifer ditching him has not only hurt him but also made Belphie hurt Satan. Belphie and Satan make amends, and the two decide to just hate Lucifer together, creating the anti lucifer league.
It'd be very in character for Belphie to blame Lucifer for the way he hurt Satan because Belphie blames humans for Lilith's death to try and alleviate his own guilt, not because he actually thinks it's their fault
At first the anti lucifer league is made out of genuine malice and spite towards lucifer but over time the two of them kinda forgive him so it becomes more of a lighthearted "younger brothers fucking with their older brother for fun" club