Compara valores de marcas de tiempo y asigna un valor a cada uno de ellos en caso de que hayan cambiado

Si entiendo su requisito correctamente, su week_switch la fila de resultados depende solo de su producto, no de su marca de tiempo.

Entonces calcúlelo en una subconsulta.

  SELECT product,
         (CASE 
          WHEN MIN(plan_week) <> MAX(plan_week) THEN 'yes' 
          ELSE 'no' END)  AS week_switch
    FROM operations
   GROUP BY product

Luego ÚNASE a esa subconsulta a sus detalles (fiddle ).

WITH switched AS (
  SELECT product,
         CASE
         WHEN MIN(plan_week) <> MAX(plan_week) THEN 'yes'
         ELSE 'no' END AS week_switch
    FROM operations
   GROUP BY product
)
SELECT
operations.time_stamp,
operations.product,
operations.plan_week,
switched.week_switch
FROM operations
LEFT JOIN switched ON operations.product = switched.product
WHERE time_stamp in ('2020-01-01', '2020-03-15')
GROUP BY 1,2;