The quote I came across was:
Twitter’s board was negotiating with Mr. Musk into the early hours of Monday over his unsolicited bid to buy the company
as the preposition "into" denote movement or a rout by which somethigs may arrive at a particular destination I tend to interpret this headline as a negotiation thta began before early hours of Monday maybe even started at sunday night or dawn and prolonged until early hours of Monday. But I read the article all the way down and it gives me a feeling the meeting started itself in the early hours of Monday. Am I getting "Into" wrong?