Rewrite documentation and publish it to github-pages using mkdocs

[Lee-W]

Types of changes

• Other (please describe)
  • documentation and CI

Description

• ci(makefile): add build-docs and serve-docs targets to the makefile
• docs: remove manually built table of contents
• ci(github-actions): add doc publish action
• docs: rewrite documentation, fix typos, and introduce spell-check to avoid typos

Checklist

• Add test cases to all the changes you introduce
• Run make lint and make test locally to ensure all linter checks and testing pass
• Update the documentation if necessary

Steps to Test This Pull Request

Expected behavior

Related Issue

Additional context