When I change the Python version, the version in the system does not change

Question

I have a problem which is related to system python version vs global/local python version. I use Python version manager, my purpose here is to create a virtual environment and use different Python versions in different projects.

birolakanesen@Birols-MacBook-Pro ~ % python --version
Python 3.9.6
birolakanesen@Birols-MacBook-Pro ~ % which python
python: aliased to /usr/bin/python3
birolakanesen@Birols-MacBook-Pro ~ % pyenv versions
  system
  3.10.13
* 3.11.7 (set by /Users/birolakanesen/.pyenv/version)
birolakanesen@Birols-MacBook-Pro ~ % which pyenv
/opt/homebrew/bin/pyenv

But I'm having a problem here. The Python version that the system sees appears to be different from the local Python version that I changed via Pyenv. I expected it to look the same on a project by project basis.

birolakanesen@Birols-MacBook-Pro Projects % pyenv local 3.10
birolakanesen@Birols-MacBook-Pro Projects % python --version
Python 3.9.6
birolakanesen@Birols-MacBook-Pro Projects % python --version
Python 3.9.6
birolakanesen@Birols-MacBook-Pro Projects % pyenv versions
  system
* 3.10.13 (set by /Users/birolakanesen/Projects/.python-version)
  3.11.7
birolakanesen@Birols-MacBook-Pro Projects % 
birolakanesen@Birols-MacBook-Pro Projects % which python
python: aliased to /usr/bin/python3
birolakanesen@Birols-MacBook-Pro Projects % which pyenv

When I change the Python version on the local side, how can I see the version I changed with the python --version command?