Hi Pepque,
Thank you for posting in the Apple Support Communities. It sounds like you’re seeing a prompt to set up an Apple Watch in the Bluetooth settings on your iPhone even though you’re not pairing with an Apple Watch. I’d love to share some information that should help.
First, make sure you're taking each of these steps to pair your Bluetooth device to your iPhone:
Pair a third-party Bluetooth accessory with your iPhone, iPad, or iPod touch
Next, try restarting your iPhone:
Restart your iPhone, iPad, or iPod touch
If the issue persists, check for an iOS update in Settings > General > Software Update. If you see an available update, make sure your device is backed up to iTunes or iCloud, then update to see if the issue persists. The steps here can help you complete this step:
Update your iPhone, iPad, or iPod touch
Lastly, try resetting your network settings. This resets Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you've used before. If you use the iCloud Keychain feature, this will reset this information on all devices that use that iCloud account and Keychain. As mentioned above, be sure you have a recent back up before completing this step. When you’re ready, go to Settings > General > Reset > Reset Network Settings.
I hope this information is useful. Kind regards.