What I'm really talking about when I'm talking about the threat of extended unemployment is the threat of losing socioeconomic class. So much depends on class: where you live, what you eat, where you worship if anywhere, where your kids go to school, who your friends are. Almost everything. It's very difficult to diversify your social and professional network outside of your class.
In most cases switching from one tech job to another will keep you in the same middle-to-upper-middle class even if you have to take a relatively large pay cut. You can even lose your job without something else lined up and it's not a big problem as long as you're confident you'll find something similar soon.
All of that is at risk with extended unemployment or being forced to indefinitely work for lower pay in a different field. Consider all the life changes someone might have to make if they have to change from being a software developer making $150k to being a rideshare driver making $40k, after six months, a year, or five years. I don't know about buggy-whip makers but probably they'd be okay with losing their jobs if they were guaranteed equal work in the new car factories. What they really dreaded was having to work for less pay in the new factories, or becoming day laborers or similar. This is what motivated the original Luddites.
I don't think we disagree on much here. When you say "socioeconomic class", that is largely valuable because of the status it confers. When your status changes to a lower rung, it hurts. Will Storr is saying having your entire status/esteem wrapped in a single measure like socioeconomic class is unhealthy. It is much healthier to have your status spread across multiple domains so that if you lose your position in socioeconomic class, your entire identity isn't shaken.
We probably do disagree on the buggy-whip/factory point. Being a craftsman carries more status than being a cog in a factory. The reason why Henry Ford made $5/day a thing was workers were leaving in droves because the work was miserable and monotonous. High pay compensated for miserable work and lower status. I've known people who go from being "somebody" in a particular field (like the military) to being a "nobody" in a different field (like a factory). Even though they got paid better in the latter, they yearned for the former because of the lost status.
What your replies seem to confirm is how much we as a society base our identities on work, sometimes to the exclusion of so much else.
I'm referring to class as a person's conception of themselves, and others' conception of them, as someone who can live the life they're living and can expect to continue living that life. Losing this doesn't just mean the loss of some sort of social authority, of having an impressive job title at parties, but also and more importantly it can mean almost everything in that person's life changing for the worse, indefinitely: worse neighborhood, worse housing, worse medical care, worse food, worse schools and college funds, worse retirement, worse jobs, worse hobbies, worse transportation, worse life expectancy. That would devastate anyone, and it's not so much about how a person self-identifies but about how much they can afford.
By that same measure, anyone who lives in a lower socio-economic class would have a lower sense of well-being. This is true for people with extrinsic work orientation, but not to those with intrinsic orientation. Again, a lot of it comes down to one's relationship with work.
People who are forced to receive worse medical care, for example because they can't afford necessary medicine anymore, are tangibly worse off than they were before. It's not a sign of an unhealthy relationship with work if someone is upset at not being able to buy medicine. Framing it that way is unhelpful.
In most cases switching from one tech job to another will keep you in the same middle-to-upper-middle class even if you have to take a relatively large pay cut. You can even lose your job without something else lined up and it's not a big problem as long as you're confident you'll find something similar soon.
All of that is at risk with extended unemployment or being forced to indefinitely work for lower pay in a different field. Consider all the life changes someone might have to make if they have to change from being a software developer making $150k to being a rideshare driver making $40k, after six months, a year, or five years. I don't know about buggy-whip makers but probably they'd be okay with losing their jobs if they were guaranteed equal work in the new car factories. What they really dreaded was having to work for less pay in the new factories, or becoming day laborers or similar. This is what motivated the original Luddites.