If it can be it is in a vacuum. Almost everything is crazier than you think. Many times whenever yields work they just blindly repeat the process - it's a freaking awesome science.
This is a very good rule of thumb about modern leading edge fab technology. Imagine the craziest, most impractical, most expensive things you can come up with for methods to manufacture things. The actual processes used are crazier than that.
For a reference point, just look up how the light source for the EUV steppers work. [0] tl;dr: They are melting tin, dripping the molten tin in droplets of carefully controlled size, shooting those droplets into a vacuum chamber at 70m/s, and then hitting them simultaneously with so many lasers that they are instantly ionized and then emit radiation of the desired wavelength. And they are using this Rube Goldberg-esque contraption as a glorified light bulb. Everything is like that.
Wow. That's a lot of extra steps compared to what they do with other discharge lamps. I'm not an authority in this area and I don't know proper terminology, so forgive me if I'm mistaken here. There must be some good reasons for all of this. Probably a long list of things to do with optics, power density, and contamination.
Here is a video of a rubidium standard teardown that I like to share. There aren't many places to actually see a discharge lamp.
No but they’ll happen in an inert atmosphere, not sure about plasma etching that may require a vacuum chamber similarly to sputtering.
The only steps that absolutely require vacuum are sputtering and ion deposition (doping), depending on the wavelength used vacuum may be used/required for the lithographic exposure too but I’m not sure if it’s actually needed especially since some lithography requires submersion.
That said nothing will be done under normal atmospheric conditions, even the oxide layer will be controlled with specific oxygen rates.