"Search for a language" is shown anyway, including pages without attached interlanguage links and/or no Wikidata item. In this case, it shows "Add languages", and clicking on it displays "No languages yet" message. As a result, "Search for a language" should be displayed only on pages having interlanguage links.
Example: https://bg.wikipedia.org/wiki/Потребител:Григор_Гачев?uselang=en
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Keeping search active does not make much sense in this context where there are no languages to search.
We can consider to keep the search bar disabled (as a way for people to recognize the selector but communicate search is not available) or remove the search bar in this context.