Is there a way to see the percentage of battery life on my iPhone?

Swipe down from the top to open control centre. Battery percentage is top right next to battery icon.

if you want it on your screen all the time, you could add the battery widget. Press empty part of screen until apps wiggle, click + in top left corner, scroll down to “batteries” and click to add to Home Screen.

Battery Health is provided on the iPhone 13. What seems to be the problem when you go to Settings>Battery>Battery Health? What do you see?

Not a problem. I only discovered it myself earlier today so glad to be able to share the tip 😊

Not exactly percentage of life, but the commonly used measure of its condition: Settings > Battery > Battery Health > Maximum Capacity.