"DWD contained a Happy Birthday tease and a jam based on A Love Supreme."
This is false. The supposed 'A Love Supreme jam' is based on a jaunty two-note rhythm that happens to be the same as the famous chant in 'A Love Supreme' - not to mention half the dance rhythms ever played, Jesus - and Page does at times play the full four-note chant line, but it takes more than a single one-measure rhythmic concordance to make a jam 'based on' anything. It must feel nice to spot such things, but it's not there this time. Four notes don't make a song; context matters. The musics are totally different. C'mon now!
Like the ballyhooed NYE '95 'Fire on the Mountain' jam that Dirksen used to get monomaniacal about, this one's just (very very very brief) coincidence. I think someone was just out to win cred this time; ho hum.