When the Raspberry Pi Pico W was first launched, the hardware for using Bluetooth was built into the board, however the software side of things still needed some work.
The wait is finally over! As of 14th June 2023, and announced by Eben Upton here, you can now use Bluetooth with your Raspberry Pi Pico W using either C or MicroPython!
As per the article - if you want to get started with Bluetooth and your Pico W the best place to start is Raspberry Pi's documentation site, and the Connecting to the Internet with Raspberry Pi Pico W book, which walks you through getting started with Bluetooth LE using both the C SDK and with MicroPython.