I am running macOS Monterey 12.7.5 and it is up to date. Is there any way to update the OS to Venture 13.?

I don't see any 16" MBPs that cannot run Ventura, but...

The following Mac computers are supported by macOS Ventura:

MacBook (2017 and newer)

MacBook Air (2018 and newer)

MacBook Pro (2017 and newer)

Mac mini (2018 and newer)

Mac Studio (2022)

iMac (2017 and newer)

iMac Pro (2017)

Mac Pro (2019 and newer)

macOS Ventura system requirements: Can your Mac run macOS 13? (idownloadblog.com)

Visit the App Store & put this in the search bar…

macos ventura

Further to BDAqua's post -

If your Mac is qualified for macOS Ventura, you can download the installer here => How to download and install macOS - Apple Support

Ventura's October 24, 2022 release! - Apple Community

Covers in more detail what you might need.