There is no official way to turn off the Python deprecation warning that you are encountering as a result of the most recent release of the Google Cloud SDK. Instead of the outdated Python 3.5-3.7 versions, you can set up the Cloud SDK to use your current Python 3.10 installation.

python3 --version

Python 3.7.6

$ brew install python3

On macOS/Linux:
export CLOUDSDK_PYTHON=/path/to/python3.10

example :
python is /usr/bin/python
python is /usr/local/bin/python

for me :

$  export CLOUDSDK_PYTHON=/usr/local/bin/python3.8