Shouldn’t the vacuum insulate the glass from the heat of the burning filament?
Don’t worry, it has zero effect on global warming. These are timescales so vast, humanity will have either wiped itself out or evolved into something unrecognisable long before the sun starts expanding.
Global warming is something that operates on the order of decades or centuries.
If we manage to stop global warming and maintain or better yet repair the state of our climate afterwards, it will take roughly a billion years for the sun to get 10% hotter and boil off our oceans regardless of what we do and longer yet for it to start its red giant phase.
To put that in perspective, a billion years ago life on Earth was all single celled.
global warming is definitely something it makes sense to worry about and which there’s still some chance to mitigate the worst effects of.
The sun expanding - or even the much earlier effects before that happens, as the sun gets hotter - will happen on such long time scales that there simply won’t be any humans at all; most species only last about a million years or so, vastly less time than we’re talking about.
We might well make the planet nigh uninhabitable in considerably less than one-millionth of the sun-being-a-major-problem time. It’s like worrying about the bridge maybe rusting dangerously a few decades from now, while not paying attention to the truck that has just veered onto your side of the road and will surely hit you in the next few seconds. You need to take evasive maneuvers, not worry about the bridge.