JavaScript: set `type: facet` parameter earlier in the request

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Describe the problem

From #695

This is based on an assumption, but if I'd implement this endpoint in the search engine, I would shortcut to the facet search as soon as I see type: facet, so this has a chance to be imperceptually faster

by @Haroenv

Describe the solution

We already have some manipulation to support the legacy signature of the search method, so we can set the type: 'facet' parameter earlier in the query