feat: add BIP example

[flxrcz]

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[Copilot]

Pull Request Overview

This PR updates the project to use the correct module name ls_mcmc (with underscore) instead of lsmcmc throughout the documentation, adds new dependencies for scientific computing, and introduces comprehensive documentation for Bayesian Inverse Problems.

• Updates all module references from lsmcmc to ls_mcmc in documentation
• Adds scikit-fem and scikit-learn as dev dependencies for PDE examples
• Introduces new BIP tutorial demonstrating MCMC sampling for a 1D Poisson equation inverse problem

Reviewed Changes

Copilot reviewed 4 out of 6 changed files in this pull request and generated 3 comments.

File	Description
pyproject.toml	Adds scikit-fem and scikit-learn dependencies; extends linter ignores for examples
mkdocs.yml	Adds BIP usage documentation to navigation
docs/usage/usage.md	Updates module references from lsmcmc to ls_mcmc
docs/usage/BIP.md	New comprehensive tutorial on Bayesian Inverse Problems with MCMC sampling

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