Why didn’t my iCloud back up save my passwords to my apps

This needs to be turned “on”

Set up iCloud Keychain - Apple Support

See also:

What does iCloud back up? - Apple Support

I have password continuity issues, on occasion, across my two devices. Assuming you're using finger or face scan, try going into "passwords" and delete the password and username associated with the problem app. Then sign into your app, but go through the reset password prompts. Permit your device to generate and store a new complex password. Permit Keychain to save your new password, and then boom. You might have continuity across your devices, and you'll see a new password stored in "passwords" across all devices.

Alternatively, some websites are difficult. Squarespace and Chase bank either don't like any changes, or prefer access from a primary device only. At least that has been my experience with them.