Idk, guess I wouldn't be too worried about the batteries like that on the original pics. Much worse dangers around a shop depending on the shop you're working in. Buddy of mine used to religiously light a cig when getting ready to drop gas tanks with the car up on the lift over top. Don't think I'd have been overly concerned about the juice either, that shop doesn't look half bad at all for cleanliness.
Don't trust my habits though, I'm a bit odd. If it came down to eating something with my hands after working on a car, I was more concerned with washing my hands after being on the interior of the car vs under the hood. Germs from grubby hands, sneezing etc = soap. Grease? Meh, it's all good. lol. For what it's worth there's plenty that gets inhaled around a shop whether vaping or not. Brake dust, brake cleaner, rubber from grinding on tires, turning rotors. Definitely wouldn't recommend vaping around the brake lathe, it's bad enough by itself. Always get that nice iron taste for awhile lol.