When I had the previous iOS version it used to ask me to remember or update the password. Now when I log into google or any other website that it used to ask me before, it doesn't. I have keychain enabled in settings.
make sure you arent accidentally using private mode.
You dont get prompted when using Private mode.
Sites have had the ability for quite a while now to block this, I would imagine the sites you're visiting have implemented something either recently (or a long time ago, but you already have saved password data for them).
Workaround: Go to the site on your desktop and force the save password into your keychain > iCloud Keychain will then make it available to your device.
You can manually enter passwords in safari settings for sites which won't save automatically.
make sure you arent accidentally using private mode.
You dont get prompted when using Private mode.