>What if I switch browsers on my phone
>What if I get a new phone
You can let Apple sync your passkeys between devices using iCloud Keychain. Then you can create a passkey on one device and have it available on all of your devices. Google also syncs passkeys to the cloud and lets you use them on Windows (with Chrome)
>What if I change from android to iOS or visa versa
I resolve this by storing most of my passkeys in my password manager. I still store the "important" ones (like online banking) in my phone so a password manager breach doesn't make me lose my money.
>What if I need to log into the site on my Wii U's browser?
Passkeys were designed to let you have more than one, so if you have a device that doesn't let you use your password manager, then just set up another passkey.