My bad on the dates.
Obama have had personal animus toward Trump over the BC issue but it sounds like he was spying on far more people than Trump. Like Cruz as he was a potential nominee. And Mittens in 2012.
And wasn’t it the Hillary campaign in 2018 election who first raised the BC issue?
As for the public origins of Soebarkah being born over seas, the earliest to question it that I've seen comes from FARS of FR back on 3/1/2008, 1:47:59 AM
It was Hillary supporters who ramped up public exposure to it, a month or so later with an "anonymous" email.