A better way to write this query?
While your query is valid, there is a lot I would differently.


Don't use CaMeL-case names in Postgres if it can be avoided. Your unnamed entity framework may force this nonsense upon you, but I don't want to deal with the double-quote mess, so I tested with your schema after removing all double-quotes - effectively making all identifiers lower-cased.


Are PostgreSQL column names case-sensitive?

Don't use illegible or illegal column and table aliases (like "wordTexts.WordId"). That's a matter of taste and style (and sanity), but you also omitted the keyword AS where you should not and kept it where you could omit it.


Date column arithmetic in PostgreSQL query

I also formatted some more to make it easier for me to grok the query. That last part is totally optional. But use some consistent formatting style.


Arriving at this:

SELECT *
FROM   PulledTexts
WHERE  Id IN (
   SELECT w.TextIdId
   FROM   WordTexts w  -- AS can be omitted for table alias
   LEFT   JOIN UniqueWords u ON w.WordIdId = u.Id  -- LEFT JOIN might be necessary here
   WHERE  u.WordText = 'automate'
   OR     w.TextIdId IN (
      SELECT w.TextIdId  -- AS and1 -- column alias only documentation here, not visible
      FROM   WordTexts w
      JOIN   UniqueWords u ON w.WordIdId = u.Id  -- LEFT JOIN misleading here
      WHERE  u.WordText = 'audit'

      INTERSECT
      SELECT w.TextIdId  -- AS and2  -- but don't omit AS for column alias
      FROM   WordTexts w
      JOIN   UniqueWords u ON w.WordIdId = u.Id
      WHERE  u.WordText = 'trial'
      )
   );


Which can be simplified to:

SELECT *
FROM  (
   SELECT w.TextIdId AS Id
   FROM   WordTexts   w
   JOIN   UniqueWords u ON w.WordIdId = u.Id  -- now we don't need LEFT any more
   WHERE  u.WordText = 'automate'

   UNION
   SELECT w.TextIdId
   FROM   WordTexts w
   JOIN   UniqueWords u ON w.WordIdId = u.Id
   WHERE  u.WordText = 'audit'

   INTERSECT
   SELECT w.TextIdId
   FROM   WordTexts w
   JOIN   UniqueWords u ON w.WordIdId = u.Id
   WHERE  u.WordText = 'trial'
   ) w
JOIN   PulledTexts p USING (Id)


We do not need additional parentheses because, according to the manual:


  INTERSECT binds more tightly than UNION. That is, A UNION B INTERSECT C will be read as A UNION (B INTERSECT C).


But this will be faster when replacing multiple intersected subqueries:

SELECT *
FROM  (
   SELECT w.TextIdId AS Id
   FROM   WordTexts   w
   JOIN   UniqueWords u ON w.WordIdId = u.Id
   WHERE  u.WordText = 'automate'

   UNION
   SELECT TextIdId
   FROM   WordTexts w1
   JOIN   WordTexts w2 USING (TextIdId)
   WHERE  w1.WordIdId = (SELECT Id FROM UniqueWords WHERE WordText = 'audit')
   AND    w2.WordIdId = (SELECT Id FROM UniqueWords WHERE WordText = 'trial')
   ) w
JOIN   PulledTexts p USING (Id)


The INTERSECT part can be cast as relational division problem. Explanation in this related answer from just yesterday:


Counting with multiple joins


db&lt;>fiddle here

Most important for performance is to have the right indexes. You probably should have a UNIQUE constraint on (WordIdId, TextIdId) in table WordTexts, which implements the currently missing index on those two columns in this order.


Does creating a unique constraint on a Postgres column remove the need to index it?