Workflow to do a complete validation of documentation changes against the Camel website

### Description

This is a follow up from https://github.com/apache/camel-quarkus/issues/6041.

While the current workflow is doing the basic format validation it could be nice to if all the checks could run.
There are some limitations on this full check (see https://github.com/apache/camel-quarkus/pull/7891#issuecomment-3443593279).

It might be worth a POC with some added changes in camel-website build commands.

Start by reviewing follow-up issue #6041 and the limitations noted in PR #7891's comment, then inspect the current documentation-validation workflow and the camel-website build commands. Done means a proof of concept that runs the complete applicable checks, with the known limitations documented.

Written by the indexing model from the issue text.