Is macOS Monterey is compatible with MacBook Pro (14-inch, M2, 2023) ?

You could run Monterey in a Virtual Machine as a guest operating system on Ventura. You might consider configuring the guest on a fast external drive via USB 3.2 Gen 2 (e.g. Crucial X8 1050 MB/s). Parallels Desktop 18.* can do this for around $120/yr subscription. Although you could squeak by on a 16 GB config, a 32 GB (or higher) RAM configuration on the M2 Max would be better as Monterey is thirsty.

As has already been alluded, you cannot run a version of macOS earlier than what the hardware shipped (Ventura).

That model first shipped with macOS 13.0 (Ventura), so you can't run anything earlier on it.