Stress
The level of stress one has really depends on two things: the amount of experience the stenographer has, and what kind of work the stenographer is stenographying (not a word). On average, this isn't the most stressful job in the world, but that doesn't mean it isn't without its less-than-stellar days.
You'll have those days where your back hurts or your fingers ache, but you have a job to do so you push through. Typically, this will be a nine-to-five job, so your hours will be much like the rest of the world and involve many of the same lifestyle benefits (weekends) and drawbacks (fewer streaming TV-binging sessions). Freelance work may let you build your own schedule as a stress reliever, and if you're a night owl you could always work in Night Court.
If you do transcribe in a courtroom, likely there will be cases from time-to-time that are unsettling, or uncomfortable, or involve bad people doing bad things. Make no mistake: Criminal court reporting will require a strong stomach. That is the unfortunate nature of the beast. However, no one is holding you at gunpoint forcing you to work in court. There are a lot of other places for stenographication (also not a word, but it should be).