A "passkey" is a bunch of metadata and a public/private keypair. It doesn't do anything by itself, of course. A physical device, like a Yubikey or a Titan, doesn't have Bluetooth. For phones and tablets these keys do support NFC but that's a whole different story.
The Bluetooth connection is how your phone exchanges the key and authenticates you through the computer. In its most secure phone, the key never leaves the dedicated security hardware/trusted execution environment that protects your key from snooping, the same way you cannot get a physical U2F key to give you the private key bits.
You scan a QR code to set up the pairing/connection process (if you haven't already), then a Bluetooth Low Energy exchange happens. You confirm you want to sign in on your phone (so you don't get tricked into scanning a QR code), then the cryptography happens that authenticates you.
You can find the protocol here: https://fidoalliance.org/specs/fido-v2.0-ps-20190130/fido-cl...
It should be noted that, at least on Android, any credential manager app will support this exchange. The passkeys in the Bitwarden app on my phone work just like the native Android key store when scanning a QR code, for instance, and other apps will also work. You can switch authenticator apps in the pop-up, or set a dialog in the Android settings if you want to switch the default.
Furthermore, there are also CTAP2 implementations for smartwatches (at least for Android smartwatches) that let you authenticate with a tap on the watch. That flow doesn't use a QR code for obvious reasons, you would need to manually connect your computer to the watch before it works. I believe https://github.com/fmeum/WearAuthn is the prime open source example of this feature.
