Você pode usar
exists
:SELECT * FROM
(SELECT
'[{"id":1,"msg":"testing"},{"id":2,"msg":"tested"},{"id":3,"msg":"nothing"}]'::jsonb as data)
as jsonbexample
WHERE
EXISTS (SELECT 1 FROM jsonb_array_elements(data) as j(data) WHERE (data#>> '{msg}') LIKE '%est%');
Para consultar a tabela conforme mencionado no comentário abaixo:
SELECT * FROM atable
WHERE EXISTS (SELECT 1 FROM jsonb_array_elements(columnx) as j(data) WHERE (data#>> '{msg}') LIKE '%est%');