Currently Online 
Honestly I think this is all overblown, I think what happened is more likely this. Yes, they have encountered an issue with split-screen on Series S but it's not a major deal like everyone is making, it's likely just a typical development difficulty, Larian themselves have said it's not an "issue" per se, it will simply just take a little bit more time and work.
I think they had a release date in mind (August 31st - original date) but they knew Starfield would release around the same time and thus focused on PC/PS. Once they knew Starfield's release date (Sep 1st - Sep 6th) they (an extremely rare move) brought forward their PC release date by almost a month to avoid Starfield on PC and release before it (smart move).
Course the Xbox version can't be ready due to the issue but I think they've simply prioritised PC/PS because it makes the most sense, they won't be in a major rush to launch BG3 on Xbox until they get some distance from Starfield, the date is irrelevant for PS as PS doesn't have Starfield, I think Sony just saw an opportunity to have a PR moment and asked them to move it back a week, same date as Starfield.
Vast majority will play it on PC as well, so ideally the focus is on launching before Starfield on PC, let Sony market boost BG3 on PS through the console wars, release BG3 a bit after Starfield on Xbox (possibly via Game Pass...) and they've staggered it out fairly well, avoiding potential competition and also had extra boosted marketing for consoles cause the console wars.
So there is an issue, but I think they've also prioritised PS/PC due to Starfield's date, they might as well avoid it and take their time with Xbox.
