I know Khan is an augmented genius or whatever, but I'm not sure how he'd be able to do that while on Ceti Alpha 5.
I have no idea why you're bringing Khan up. He's not involved in this story at all.
If what we're told in Picard is accurate, no one would've been sabotaging the Enterprise's transporters immediately after BOBW.
Yeah, no. No one claimed they were. The rogue Changelings are the ones hacking into the Starfleet transporter systems, and they were clearly doing this for an indeterminate period of time. We don't know how long ago the plan was initiated or how long the Changelings have been infiltrating Starfleet, but it probably was no earlier than PIC S1 (2399).