With Nate and Hank we’ve also seen the soul can sometimes hang around for a while after death watching things so it’s not clear to me it couldn’t still be there to jump in a new clone body given the opportunity.
That bugged me because there was no apparent weight to it so it was clearly an empty pizza box (aka the empty coffee cups shows use all the time) and if it had been real the pizza would be all messed up from not keeping it horizontal.
Also the courtroom stuff was silly. But padding your pizza box so it has weight and treating it like an actual pizza should be so easy.
If you go back and watch the actual footage he showed them it was stuff we saw here like Wanda using her powers to open the doors into SWORD so it looks like she forced her way in and her bursting through the glass to fly down to Vision’s body. Hayward just says she took the body.
The thing that bugged me was the storty where Saru claimed they were descendants of the ship's original Starfleet crew members. The story doesn't stand up to much examination and even if it had if things go well talking to Earth you're eventually going to have to come clean. Telling them you've traveled from the past would have been a simple enough explanation and still allowed Saru to omit information he didn't want to go into yet without actually lying.