Unable to pair MacBook Pro with my iPhone 16 Pro Max via Bluetooth

Macs and iPhones do not pair using Bluetooth. Sometimes they use Bluetooth for Continuity features – but not in a traditional pairing way.

As far as getting Macs and iPhones together, there are many ways to do so, including

• Synchronization through iCloud (iCloud+ - Apple ; Set up iCloud on all your devices - Apple Support). You get 5 GB of storage free; beyond that, you need to subscribe to more via an iCloud+ or Apple One plan.
• Synchronization through connections to the same e-mail accounts (whch can have associated calendars).
• Continuity features (Continuity features and requirements for Apple devices - Apple Support). These include a very wide assortment of features; I'd suggest reading the Support article for descriptions.

Other links that may be of interest:

Sync your iPhone, iPad, or iPod using your computer - Apple Support

Transfer photos and videos from your iPhone or iPad to your Mac or PC - Apple Support

iPhone User Guide - Apple Support

Mac User Guide - Apple Support

iPhones don't pair to Mac like headphones do. They never have.

If you're trying to sync info between the two, you use iCloud and your AppleID Account, or you connect the two with the charging/sync cable and look for the iPhone in Finder.