I don't claim that my impression is the authoritative truth about what the text of the Bible says, but overall to me it is surprising how little detail is provided in the Bible about an afterlife. At the time of Jesus, the Jews were sharply divided as to whether there was any afterlife at all. The Pharisees said there was an afterlife and the Saducees said there was not. I take that as an indication that the "Old Testament" does not give a consistent authoritative answer.
It was clearly the pop-cultural obsession of Jesus's time, but there was no clear religious unified position on it.
I'm pretty clear that when Jesus talked about the kingdom of heaven he, at least usually, meant the new way of doing things that he wanted to encourage here on earth during our usual lifetimes. We are told that he did make a definitive statement on one occasion that there is an afterlife - supporting the Pharisees against the Saducees - but most of the time he was talking about changing how we do things in this life. Given how little he talked about an afterlife, it wouldn't surprise me if somebody just threw that into the text later, slash fiction style, because they wanted him to have said something about it.