Will new Mac Bluetooth Magic Mouse work with my MacBook Pro ?

Sorry, no.

See the Compatibility section of Magic Mouse (USB‑C) - White Multi-Touch Surface - Apple

Also see the following from that same website:

System Requirements

Mac with macOS 15.1 or later

iPad with iPadOS 18.1 or later

A 2013 MacBook Pro cannot be upgraded beyond macOS 11.x Big Sur

Partially.

It will pair and generally work, but.....

You won't have anywhere to plug it in to charge it. You will need a USB-C to USB-A adapter, a usb-c to usb-a cable or a USB-C charging brick.

Also, on Mac's not running macOS 15.1 Sequoia or later, the 2 finger scrolling feature and likely other gestures on the mouse surface seem to not work properly or at all.