First of all; Yes, that is definitely the belt from Cas’ trenchcoat sticking out from under/inside of Dean’s duffel (because we’ve just seen Sam start packing his duffel which is right next to it, right?). It’s the wrong colour to be part of either of their bags, so.
Then; four thoughts struck me while watching this.
One: it’s actually not strange at all that this imagine exists; during the early seasons Sam and Dean (or well, mostly Dean) were wanted by the police, and someone could easily have snapped a candid photo of them at some point. It’s also not strange that Cas now has it, since hey, angel powers of pretty much amazing? He could hunt down and collect that, no problem.
Two: Sam is hella smart; he’s probably seen Dean pack the coat into the car (their multiple cars, this season) and he probably draws the same conclusion as we when seeing this photo: this was in Cas’ trenchcoat. Imagine how terrible he must feel knowing that the last things he did when seeing Cas was
- To accuse him of leaving his soul behind in Hell deliberately
- Stab him in the back and try to kill him
Three: If the photo is laying exposed like this, it has to have moved from inside the trenchcoat. My theory? Dean found it. He probably went through the coat at some point, perhaps in a moment of drunken desperation, in order to try and find something, some last piece to the puzzle, something that could explain why Cas felt the need to go behind their backs, why he “betrayed” them, as they think of it.
And then he found this picture. It’s a picture of Dean and Sam from the time before they carried the weight of the world on their shoulders. Dean must know there aren’t many other pictures around of the two of them, but that definitely still means something. Cas didn’t want to put this - the civil war in heaven - on them, too. They’d done enough. They deserved some peace. And he thought that by leaving Dean at Lisa’s and pulling Sam out of Hell (since he didn’t know at the some that he’d forgotten a piece), he’d be able to give them that.
And Cas was/is Dean’s best friend. No matter how much he didn’t want to listen to his so-called “excuses” at the end of Season 6, he must still have understood somewhere deep down that this was his intent. By finding this picture, by realising that this was what Cas used to remind himself of Dean and Sam during his time away fighting his brothers in Heaven, he must have drawn the same connections, because he knew Cas, and he also knows how it feels to want to spare someone any possible pain because you love them too much.
Four: Upon finding the picture laying around like this, Sam probably understands that Dean has found it as well, and despite now knowing Cas as well as Dean did/does, he knows Dean better than anyone, and thus he most likely understands how devastating finding this picture was for him as well.