does anyone still have a copy of that 4chan thread where the OP was claiming to be a member of the US Intelligence community and claimed that Hillary and Obama would rather go to war with Russia than reveal the contents on Huma Abedin's laptop?
When Snowden came out with everything that he was willing to share, he also said that they were spying on everyone, and that the reason for the spying had nothing to do with terrorism, catching terrorists, or stopping terrorist, it actually was more useful as a tool for the government to know everything that was going on with major corporations, before they made anything public. So it's sort of like corporate spying.
Sure, they can use it to monitor terrorist, but I don't believe it really has any function that is really relevant to stopping terrorism.
So sure, of course Obama could have spied on everything that Trump did in or near an electronic device.
The only thing stopping Obama from doing so would have been his own discretion. Of course we will never get the proof that Obama actually did it, if he did. So there's no use even worrying about it.