I’m not sure what these rooms control, but it’s possible the control room is simply part of a greater facility that has a mandate for this. Which makes sense, since there’s something to control here that may be more sensitive / dangerous than the control room itself.

Nuclear power plant. Workers would wear those uniforms while on site so that they don't track any stray radioactive particles home on their street clothes.

Slightly different environment, but my dad was a service engineer in the 1960-1980s mainly working on coin counting equipment. His workwear for customer sites was a white coat over his suit. That was fairly normal back then so probably kept to traditions in industry. I've nothing to add about the hat though.

I've not got a photo of him at work, but this is him wearing one of his old & dirty coats after he retired.

https://www.flickr.com/photos/stevecargill/52576937191/

Probably because nuclear plant workers were thought of as lab workers, and those wore these uniforms as well. Not sure if it was also a precaution against hair and threads falling into critical equipment.