[tox] Update doc testenv to account for documentation restructuring
* Build doc from `doc` directory.
* Use `sphinx-build` directly instead of `make` as this now works and allows
to build within .tox temporary environment (instead of doc/_build),
preferable for a "test" action.
Related to #5447161.
Experiment with the search bar. Try queries like "card sometextualcontent" or
"card wikiid index" or "345".