Postgres 14

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drop table if exists my_table;
create table my_table(id int primary key, access jsonb);
insert into my_table values
(1, '[{"id": 1, "user":"user1", "permission": 1}, {"id": 2, "user":"user2", "permission": 3}]'),
(2, '[{"id": 1, "user":"user1", "permission": 3}, {"id": 2, "user":"user2", "permission": 7}]');

DROP TABLE

CREATE TABLE

INSERT 0 2

drop table if exists my_table;
create table my_table(id int primary key, access jsonb);
insert into my_table values
(1, '[{"id": 1, "user":"user1", "permission": 1}, 
      {"id": 2, "user":"user2", "permission": 3}]'),
(2, '[{"id": 1, "user":"user1", "permission": 3}, 
      {"id": 2, "user":"user2", "permission": 1}]');

DROP TABLE

CREATE TABLE

INSERT 0 2

select *
from my_table
where jsonb_path_exists("access", '$[*] ? (@.user == "user1")')
and jsonb_path_query_first("access", '$[*] ? (@.user == "user1").permission')::int & 2 = 2

id
access

2
[{"id": 1, "user": "user1", "permission": 3}, {"id": 2, "user": "user2", "permission": 1}]

SELECT 1

select t.*
from my_table t
cross join jsonb_array_elements(access)
where value->>'user' = 'user1'
and (value->>'permission')::int & 2 = 2

id
access

2
[{"id": 1, "user": "user1", "permission": 3}, {"id": 2, "user": "user2", "permission": 1}]

SELECT 1