MySQL 8.0

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CREATE TABLE allemployees (schedule JSON, name_cyr VARCHAR(255))
SELECT '[{"2022-01-03": "H 08:00"}, [{"2022-01-04": "H 08:00"}] ]' schedule,
       'John Doe' name_cyr;
SELECT CAST(schedule AS CHAR), name_cyr FROM allemployees;


CAST(schedule AS CHAR)
name_cyr


[{"2022-01-03": "H 08:00"}, [{"2022-01-04": "H 08:00"}]]
John Doe


UPDATE allemployees
SET schedule = JSON_SET(schedule, '$[0]."2022-01-03"', 'O 08:00') 
WHERE name_cyr = 'John Doe';
SELECT CAST(schedule AS CHAR), name_cyr FROM allemployees;


CAST(schedule AS CHAR)
name_cyr


[{"2022-01-03": "O 08:00"}, [{"2022-01-04": "H 08:00"}]]
John Doe