Regarding Half-Life canon...

Clearly, he kept it all the way until EP2 and put it in the rocket.

He ate the can obviously.

I personally think he didn't pick up the can, and instead noclipped through the Metro cop to the next room.

i mean if we're being real, the ending of alyx implies either a multiverse that gman can hop between to influence events at will, or the ability to time travel a la terminator by going into the past and changing the future.

option a, it's all 3 and every playthrough is a different universe. option b, a superposition of all 3 depending on what the player decides. either way all can identities are valid