Improved documentation (examples, exported APIs, playbooks, etc.)

Hi everyone,

The documentation for the current repo could benefit from more explicit guidance on how to use the APIs. In general, the repo is solid, but it is hard for "outsiders" to understand its full capabilities, which hinders its adaptability, accessibility, and usability.

Here are some examples:
- In the getting started documentation, there is $alpha$ vs $\alpha$.
- The README.md should include examples on how to instantiate Tableaux, SAT solvers, etc. Ideally, people should understand the repo's full capabilities (e.g., different solvers, formulas, and semantics).
- What exactly is exported?
- How should one use this repo?
- What are the known limitations?
- Are there playbooks/playgrounds for users?
- Etc.

These are just a few examples. Some of them are general observations that could be applied to other repos as well within the `Sole.jl` ecosystem.

Start with README.md and the getting-started documentation, since both are explicitly called out. Locate where API usage, exported APIs, solver examples, limitations, and playbook/playground guidance are currently documented and add the missing content there. No tests or code entry points are mentioned, so done looks like a documentation pass where a newcomer can understand capabilities and usage directly from README/getting-started sections.

Rédigé par le modèle d'indexation à partir du texte de l'issue.