Public docs should be user oriented

The current docs are very much describing the internal implementation details about what works and what doesn't, which is interesting, but maybe too detailed for a user.

I think we should make sure the user docs are optimized for human consumption only (internal docs can be moved to another directory in the sidecar repository). As most features are just easily discoverable in an IDE, docs can be terse and straight to the point. We should also make a clear separation between using the LSP server in an IDE and the lsp check CLI command (2 different use cases).

While rewriting the docs, don't assume the current docs are correct, double-check you check what the code actually does.

Let's do that in 3 steps:

• Let's write a local skill about writing user docs (based on the goal here) so that the docs don't drift again in the future
• Rewrite the current docs from the ground up with human users in mind
• Write good minimal internal docs, more agent-oriented

Start by reviewing the current user docs and verifying their claims against the LSP server and the lsp check CLI command. Define the local user-doc writing skill, then separate concise IDE guidance from CLI guidance and produce minimal internal docs in the sidecar repository; done means all three requested documentation steps are complete and accurate.