How do I connect my new iphone 16e to my MacBook Pro with bluetooth?

Macs and iPhones don't support Bluetooth pairing with each other.

They work together in other ways, including

• Synchronization through iCloud, shared email accounts, and third-party cloud services
• Continuity features (Continuity features and requirements for Apple devices - Apple Support)
• Manual synchronization (e.g., of music from your own CDs, from your Mac to your iPhone) (Sync your iPhone, iPad, or iPod using your computer - Apple Support)
• Shared access to subscription services such as iCloud+, Apple Music, Apple TV+, and Apple Arcade.

If you are using an Apple Silicon Mac, the App Store might offer you not just Mac applications – but some iPhone and iPad ones, as well.

Unfortunately, you can’t connect an iPhone to a MacBook via Bluetooth for data transfer or syncing. Apple does not support that function over Bluetooth.

To connect your iPhone 16e to your MacBook Pro, use these methods instead:

• Use a USB-C or Lightning cable – for syncing, charging, or using Finder (macOS Catalina and later).
• Use iCloud – to sync photos, contacts, messages, etc.
• Use AirDrop – for sharing files wirelessly between devices.
• Use Wi-Fi syncing – via Finder or iTunes (enable when both devices are on the same network).

Bluetooth on iPhones is mostly used for audio devices, not for connecting to Macs.

Doesn't really matter what Mac you have. Traditional Bluetooth pairing between Macs and iPhones / iPads are not supported......but AirDrop, AirPlay and Hotspot will work.

What is it that you are trying to accomplish?

You can connect it through your apple id. You can also connect the screen through the iphone mirroring app. If you do not have the iphone mirroring app, you could try to connect through a cable. You could trouble shoot with the screen mirroring option in the control center.