ENH: Bring `devcontainer` closer to GitHub CI environment, improve `vscode` setup
- [x] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [ ] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

This PR serves two purposes:

1. **Harmonizing devcontainer with the CI environment in GitHub Actions**
GitHub Actions use `micromamba` for Python environment management, while the old devcontainer setup used to use `pip` (with a list of dependencies fetched from `requirements-dev.txt` once at container image creation).
As I was trying to reproduce an unrelated issue locally, I was unsure whether deviations from the CI reults may have been caused by different Python environments. This change should reduce uncertainties in this regard.
2. **Modernizing the Visual Studio Code setup**
This PR attempts to produce a devcontainer that has high utility out of the box (e.g., installation and configuration of extensions for `mypy`, `flake8`, `black`, etc.)
Furthermore, it replaces deprecated configuration options with the preferred ones.

If you like this PR, please let me know which `whatsnew` file this should be mentioned in (`v2.1.0.rst` I presume?)

Also, do you need me to open an issue for this?
I see the check `docker run --rm pandas-dev-env python -c "import pandas as pd; print(pd.show_versions())"` is failing.

It did not previously because the old `Dockerfile` installed whatever `pandas` it pulled in via `pip`. I'm not sure what value this has, as I suppose the users of the docker image would be building and using their development versions anyway.

So I see two approaches here:

1. Remove the `docker run` check above, if you agree it serves little value; or
2. Have a separate CI process build and publish a complete docker image with the respective HEAD installed; this image could then be checked.

The second approach would be quite a bit more involved I think, as I don't think there is an established Docker publication infrastructure in `pandas`, is there? > Also, do you need me to open an issue for this?

I would recommend you open an issue about this first before moving further with this PR, the Dockerfile for example used to be closer to what you had but it was deemed to large/slow to build and it was slimmed down. It would be good to discuss in an issue since it might also break people's workflows Thanks for opening up https://github.com/pandas-dev/pandas/issues/54862. Closing to ensure the discussion happens in https://github.com/pandas-dev/pandas/issues/54862 first before proceeding here