I'm glad you're enjoying your coldcard. I have one too.

And yes, that phone wallet is hot as long as the private key, that value which is used to sign your transaction and make it valid to miners, is on the phone somewhere. If you lost the paper, still remembered the PIN to the app you use, and could still make a Bitcoin payment, then that's a hot wallet.

If you made a key on your phone, wrote it down, and then securely deleted the key off of your phone by, say, using Samourai wallet or throwing it into a volcano, then you'd have a cold paper wallet, which is pretty secure, but a little flimsy. Your private key only exists on that paper and nowhere else.