Removing the app does not completely uninstall that version of Python. You will need to remove the framework directories and their symbolic links.
Deleting the frameworks
sudo rm -rf /Library/Frameworks/Python.framework/Versions/[version number]
replacing [version number] with 3.10 in your case.
Removing symbolic links
To list the broken symbolic links.
ls -l /usr/local/bin | grep '../Library/Frameworks/Python.framework/Versions/[version number]'
And to remove these links:
cd /usr/local/bin
ls -l /usr/local/bin | grep '../Library/Frameworks/Python.framework/Versions/[version number]' | awk '{print $9}' | tr -d @ | xargs rm*
As always, please be wary of copying these commands. Please make sure the directories in the inputs are actual working directories before you execute anything.
The general idea in the end is to remove the folders and symlinks, and you’re good to go.
Here is another response addressing this process: How to uninstall Python 2.7 on a Mac OS X 10.6.4?