Apple is testing biometric login for iCloud.com. If you’re a beta tester for iOS 13, iPadOS, or macOS Catalina, you can go to beta.icloud.com and login with Face ID/Touch ID.
So far, iPhone and iPad users haven’t been able to access iCloud web apps. If you navigated to the website you couldn’t use anything except Find My iPhone. If you’re on a beta device and go to icloud.com you should be redirected to beta.icloud.com. If not, then just type it manually or tap on the above links.
Apple may even let users login to iCloud.com via Sign in With Apple, which will enter testing phase this summer.