Hey bigredsatyr,
We understand that your new iPhone 12 isn't offering to save your passwords, update passwords, or suggesting passwords when creating them. We want to help! First, if you open the Settings app, do you see an alert to finish setting up your account? With iCloud Keychain you'll need to approve your new device. More details about that data can be found here:
iCloud security overview
Make your passwords available on all your devices with iPhone and iCloud Keychain
You'll also want to be sure that your iPhone is fully updated to software version 14.3. To see what you have installed, tap Settings > General > About. If an update is needed, be sure to back up your iPhone first:
How to back up your iPhone, iPad, and iPod touch
Update your iPhone, iPad, or iPod touch
Update apps or use automatic downloads
Also be sure you're not using a private browsing window as you won't be prompted to save the password: Turn Private Browsing on or off on your iPhone or iPod touch
If you're still having an issue at this point, you'll want to reach out to Apple Support to look into this more: Get Support
Thanks, and take care.