docs: update theme, improve consistency, rewrite user guide

[airwoodix]

Summary

This patch is a overhaul of the documentation, with the following major changes:

• switch the theme to qiskit-ecosystem from the newest qiskit-sphinx-theme package. This also triggered the switch to Sphinx 7 and a cleanup of the docs/ subtree.
• improve internal and external linking in the API reference. Add API documentation for the transpiler plugin.
• fully rewrite the user guide and add a quick start example in the documentation landing page. The new user guide goes a bit further than the previous one and puts emphasis on good practices and common quirks. A section about the specialized Sampler and Estimator primitives will be added later.

Details and comments

Closes #58.

The nitpicky flag for sphinx is now enabled. Some of the registered exceptions could probably be solved, provided a significant time investment into the autodocs internals (it's not clear to me why adding an entry for typing-extensions in the intersphinx_mapping doesn't allow resolving the few Self instances).

Use

poe docs
<browser> docs/_build/index.html

to preview the built docs.

[alfrisch]

thanks for the great docs improvement!

[Eric-Arellano]

Huzzah!

(I didn't review the content changes, only the docs infra)

[Eric-Arellano]

This makes it so the left side bar doesn't include the word "documentation" in the site title:

Suggested change

	html_theme = "qiskit-ecosystem"
	pygments_style = "emacs"
	html_theme = "qiskit-ecosystem"
	pygments_style = "emacs"
	html_title = f"{project} {release}"

[airwoodix]

Thanks for the review!
Sorry, your review crossed the merge process. Could you please file a PR with your change?