Something on your phone is more secure ... much more secure ... because it never travels on the Internet, so it can't be stolen in transit or exposed in a data breach.
To use your passkey on more than one device, store it in a password manager, like Microsoft Edge.
The passkey on your device is stored on secure hardware separate from the rest of the hardware, so it can't be hacked by malware. And because the authentication is performed by key pairs, a passkey can't be phished and there's nothing you need to remember so it can't be forgotten.