Usually these differences are caused by the requirements of the underlying database the query is being run against, but if that is the same in both the development and the production environments, then it might be because the 10.9 REST API uses the SQL-92 standard (see second image below. It doesn't talk specifically about the REST API, but it mentions the 'date' keywork being required by SQL-92).
https://desktop.arcgis.com/en/arcmap/latest/map/working-with-layers/sql-reference-for-query-expressi...
file geodatabase use the "date" syntax
With regard to the integer queries... never heard of one working with quotes unless its stored as text in the database.