Combine varias filas con diferentes fechas con variables superpuestas (para capturar las primeras y últimas fechas de cambio)

Considere usar un LAG función de ventana y combinación de agregación condicional a través de múltiples CTE y autocombinaciones:

WITH sub AS (
  SELECT "user"
       , "type"
       , "date"
       , CASE 
            WHEN LAG("type") OVER(PARTITION BY "user" ORDER BY "date") = "type"
            THEN 0
            ELSE 1
         END "shift"
  FROM myTable 
), agg AS (
   SELECT "user"
         , MIN(CASE WHEN shift = 1 THEN "date" END) AS min_shift_dt
         , MAX(CASE WHEN shift = 1 THEN "date" END) AS max_shift_dt
   FROM sub
   GROUP BY "user"
)


SELECT agg."user"
     , s1."type" AS first_type
     , s1."date" AS first_type_initial_date
     , s2."type" AS last_type
     , s2."date" AS last_type_initial_date
FROM agg
INNER JOIN sub AS s1
  ON agg."user" = s1."user"
  AND agg.min_shift_dt = s1."date"
  
INNER JOIN sub AS s2
  ON agg."user" = s2."user"
  AND agg.max_shift_dt = s2."date"

Demostración en línea