Neither Obama nor Biden nor Bloomberg are "active government officials". They have no power to conduct U.S. government business, thus an intrusion on their private social media accounts is not going to be an obvious or immediate threat to the security of the U.S. government.
Former presidents are still privy to a lot of information (e.g. they receive national security briefings still). Hacking their technology accounts is absolutely a threat to the security of the US govt, and is one reason the Secret Service specifically monitors their technology usage.
I'd bet a lot of money the inclusion of people like Obama and Biden all but guaranteed the FBI/NSA get involved now, or at the very least the Secret Service.
It's not just about access to information, but actual power and perceived power; the chances that the average rational person will be fooled and react to "The U.S. Treasury has been ordered to fast-track the evaluation and adoption of Bitcoin as an option for official government transactions" is much higher coming from Trump, Pence, Mnuchin, McConnell, or any number of the official social media accounts of U.S. agencies than it is for Obama or Biden. Sure, the latter could most definitely fool people, but that's possible with any famous account, like Elon Musk's or Kanye's.
I think you're incorrect about the perceived power of a former US president, but regardless I don't think perceived power has any impact on whether the FBI chooses to investigate or not.
That might be a fairy tale some black hats tell themselves, but it seems clear to me that compromising a former president's accounts has serious security implications for the US govt. Obama's access to information (both past and present) is such an overriding concern that his level of perceived power is basically an after-thought.
The FBI often helps out with major breaches of all varieties, let alone ones that involve former heads of state. It's extremely unlikely they're not already involved in this one.
