Check out this Stats Tracker Guide for Genshin Impact. Learn about how to check your stats (My Battle Chronicle) at Mihoyo's webpage, how to make your stats public and more.
Table of Contents
Stats Tracker - How To Check Your Stats
There is a way to check stats of your account in Genshin Impact. The following is the step to check it.
Step 1: Login To Your Mihoyo Account At Official Forum Page

Access Mihoyo;s Genshin forum page, and input your credentials to login.
Step 2: Click "My Battle Chronicle" Option (Optional)

In case you cannot see your stats after the step 1, find "My Battle Chronicle" at your account screen. And this is it!
Step 3: Make Your Stats Public (Optional)

If you want to make your stats public, you can click Public switcher at right of the screen. Note that your account would be visible inside the Mihoyo forum & perhaps at external website if there would be APIs open to public by Mihoyo.
If you happen to know a way to track stats of others. Please share your comment at bottom.
Stats Tracker - Requirement
In order to access your stats, you need Mihoyo Account. Creating Mihoyo account is a part of the account setup for PC & Mobile but not for PS4 as far as we know. (though there might be a way to set it up for PS4).