This really has nothing to do with Big Tech and is a nearly universal characteristic of any job that requires mental effort instead of physical. Yeah, if you're getting paid to move boxes all day, the boxes don't follow you home. If you get paid to think all day, the thoughts do. Nothing much you can do about that other than learn to deal with it.
My friends who are scientists think about their research in their free time, and worry about upcoming conference deadlines, etc. My friends who are lawyers think about their cases and upcoming filing deadlines. My friends on the business and sales side think about clients and deals and marketing. That's just how it goes. Be glad someone is willing to pay you for it and that your brain doesn't wear out from thinking the way your back wears out from carrying boxes.
This person just sounds like they have trouble setting boundaries and some general anxiety issues. I am a SWE at a FANG company right now, in a reasonably important and high-profile area, and the work-life balance is way better than any other job I've had at smaller companies both in and out of "tech".