"they were so into each other" in the above sentence means they were deeply in love.
I wonder if British speakers use "into" this way colloquially. For better or worse, it comes quite naturally to me. I'd never use it in formal writing, though.23. Interested or involved in; knowledgeable about. colloq.
1969 Rolling Stone 28 Jan. 19/1 I tend to like the stuff the rock groups are doing because they're creative and original, and that's something I'm very much into.
1969 Down Beat 20 Mar. 17/1 She is a Libra, for those of you who are into that.
1969 It 4 July 15/3 He was basically into being a hustler, which he was very, very good at.
1971 Ink 12 June 19/1 This should have been the high~light of the evening, but the audience just wasn't into it.
1971 New Yorker 11 Sept. 48 First I was into Zen, then I was into peace, then I was into love, then I was into freedom, then I was into religion. Now I'm into money.
1973 Listener 15 Feb. 209/1 Margaret is ‘into’ astrology, and consults the I-Ching each morning.