demo:
begin;
SET LOCAL TIME ZONE 10.5;
with cte(s) as (select jsonb '"2023-08-15 12:34:56 +05:30"')
select jsonb_path_query(s, '$.timestamp_tz()')::text,'+10.5'::text,'timestamp_tz'::text from cte
union all
select jsonb_path_query(s, '$.time()')::text,'+10.5'::text, 'time'::text from cte
union all
select jsonb_path_query(s, '$.timestamp()')::text,'+10.5'::text,'timestamp'::text from cte
union all
select jsonb_path_query(s, '$.date()')::text,'+10.5'::text, 'date'::text from cte
union all
select jsonb_path_query(s, '$.time_tz()')::text,'+10.5'::text, 'time_tz'::text from cte;
SET LOCAL TIME ZONE -8;
with cte(s) as (select jsonb '"2023-08-15 12:34:56 +05:30"')
select jsonb_path_query(s, '$.timestamp_tz()')::text,'-8'::text,'timestamp_tz'::text from cte
union all
select jsonb_path_query(s, '$.time()')::text,'-8'::text, 'time'::text from cte
union all
select jsonb_path_query(s, '$.timestamp()')::text,'-8'::text,'timestamp'::text from cte
union all
select jsonb_path_query(s, '$.date()')::text,'-8'::text, 'date'::text from cte
union all
select jsonb_path_query(s, '$.time_tz()')::text,'-8'::text, 'time_tz'::text from cte;
commit;