Why isn't a binary not being found in my PATH?
The only way I found to reproduce what you are seeing is if the symlink points to a non-existing file. So best to use ls -l to verify that all the symlink targets actually exist, and fix the links if necessary.

More generally speaking: Unless you really need a specific version of python3 it might be better to just run

cd /Users/dalemy/Projects/my_project/bin
ln -s /usr/local/bin/python3 python3


or just rely on PATH.