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Pragma compile_options does not show some options
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I cannot state the causality. But I can see a reasonable rationale which is why I elected to not treat this omission as a bug.

Most (if not all) of the compile options which appear in "pragma compile_options" relate to capabilities and capacities.  The two bits encoded into SQLITE_DQS are different in that they specify a pair of deviations from standard SQL syntax rules which are to be allowed or disallowed. Neither affects how correctly written SQL is compiled or how such SQL will perform. They therefore have have less utility for applications which may need to ensure a feature is present or a capacity suffices.

If there is a good case for its inclusion in that pragma's output, this would be a good place to present it.