Is /usr/bin/python3 provided with macOS Catalina?

Kinda. A clean installation of Catalina includes a /usr/bin/python3 binary, but it's a stub for installing the command line developer tools, which includes Python 3.

If/when the command line developer tools are installed, the /usr/bin/python3 stub will run the actual python3 binary, but a clean install will just have the stub.

The Python 2 binaries (/usr/bin/python /usr/bin/python2) are still present on a default installation, but they are deprecated and the warning message says they will be removed in future versions.

Yes - that file is part of the system image and ships on every Mac.

When fully installed, version 3.7.3 is what Catalina installs from this stub. Keep in mind python 2.7.16 is still the default python if you don’t call python3

    ~ % /usr/bin/python3 --version
    Python 3.7.3

    ~ % /usr/bin/python --version
    Python 2.7.16

     ~ % sw_vers
    ProductName:    Mac OS X
    ProductVersion: 10.15.5
    BuildVersion:   19F101