When you're looking at the Steam Deck you may come across the G-Man easter egg, Well known by this point, We can clearly see that the G-Man is smoking a pipe on the picture, Weird of Valve to give us a tiny Lore piece like this, There are so many questions about him we don't know yet and they decided to Spill the Beans that he is a smoker of all things? This gives us only more questions like what's he smoking?
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Honestly, probably a reference to the Cigarette Smoking Man from The X-Files. Both of them are pretty mysterious fellows, and both have a big impact on the MC and story. Main difference: Gman likes pipes.
Also, it's more than likely just cool art that Valve thought It'd be funny to add in as an Easter egg
In my expertise, A universe like this that does have a confirmed case of parallel realities and different timelines, An all-powerful being like him who has control over these things doesn't have coincidences nor random appearances.
Explains the voice and his appearance in Half-Life 2.
Indeed he does have some heavy breathing occasionally