In the expression of our searchVector fields, we use the "simple"
configuration (over the default "english" one), to avoid picking a
language that's irrelevant to the user.
I initially forgot to add the same configuration to the query that is
being sent using ts_query.
Adding it will also allow the search to work for a single character,
while so far a single letter was most of the time considered a "stop
word" (a word with no semantic value, like "a").
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