Hello and welcome to Apple Support Communities nycrel,
We see that you're having an issue with your Apple Watch not reading the amount of flights of stairs you've climbed the way that it does on your iPhone. We certainly understand wanting to see accurate measurements, and we'd be happy to help.
You've already done some good troubleshooting by unpairing and pairing the devices back together. Next, we'd like to have you go through the steps in the articles below to calibrate your Apple Watch to get accurate measurements.
Calibrating your Apple Watch for improved Workout and Activity accuracy
Get the most accurate measurements using your Apple Watch
Also, are you using Fitness+ when this is happening?
We look forward to hearing back to from you.
Have a wonderful day!