LuxGiammi's answer is correct with good advise.

RE: how to accurately install Python packages? Should I use pip, pacman or yay?

(1) User or Virtual Environment: Great for development.

There is a dozen virtual environment managers available.

I recommend pyenv:

• Upside: Reliable and rarely breaks. Does not require root.
• Upside: Excellent support of multiple, distinct Python environments. Easily install any combination of Python and libraries through pip.
• Upside: Can specify version requirements.
• Downside: Requires setup. Is an additional, distinct tool for package management.
• Downside: Few protections or official support from Arch.

Example:

# Install pyenv and install desired Python version directly into user directory:
$ pacman -S pyenv
$ pyenv install 3.12 # Builds Python version specified

# Select which python version or environment you would like to use:
$ pyenv [local|global] 3.12 

# (Optional) Point pycharm to your environment. e.g. ~/.pyenv/versions/3.12/bin/python
# (Optional) Create virtualenvs

• PyEnv on GitHub - Has complete instructions
• RealPython.org - Intro to PyEnv

(2) System-Wide: Arguably a more accurate method. Clean, distributable.

Installed with pacman or an AUR helper such as yay. Easy and great if your project already has packages.

• Upside: Software managed by one package manager. Arch packages are officially supported.
• Downside: It may be difficult to specify desired version dependencies.
• Downside: Third-party Python AUR packages may break and need re-installed when Python is updated.
• Downside: Security or stability concerns with obscure third-party libraries installed to OS.
• Downside: Some PyPi third-party packages have neither an Arch-repository or AUR package. You could try a PKGBUILD Generator.

RE: Is it necessary to add the python- prefix?

Recommended and you should, but not required.