I was. But (a) a lot of things are subsidized as a grad student (my dorm room rent was 30% of market price for the area), and (b) savings are nearly zero. It's close to a paycheck-to-paycheck life unless you have some external income (which I did, via Google Ads that I slapped on a 250K MAU/month website of mine). That external income paid for me to eat healthy, buy outdoor exercise equipment, have a couple shoestring budget vacations per year for mental health, etc.

I'd consider "being able to save enough to continue a modest quality of life for retirement" a normal feature of what describes middle class life.

If you are living paycheck-to-paycheck you'll suffer when you hit old age or have a disabling condition that prevents you from working.