One option would be using below approach containing JSON_LENGTH(), JSON_EXTRACT() and JSON_SEARCH() functions together even for the version 5.7 (5.7.13+) where an array(js) extracted in the subquery and they're splitted to individual array for each values (true and false) by using JSON_SEARCH() function containing all as the second argument, and then counted by JSON_LENGTH() function :
SELECT ID,
JSON_LENGTH( JSON_SEARCH(js, 'all', 'true') ) AS Cnt_True,
JSON_LENGTH( JSON_SEARCH(js, 'all', 'false') ) AS Cnt_False
FROM ( SELECT *, JSON_EXTRACT(jsdata, '$.*') AS js
FROM tab ) t
provided JSON field has quoted values such as "true" and "false"
JSON_EXTRACT(jsdata, '$.*') still can be used in case that the boolean values are unquoted as in your case. But, this time some string operations would be needed. Here, I preferred using CHAR_LENGTH() function :
SELECT ID,
CHAR_LENGTH(js) - CHAR_LENGTH(REPLACE(js, 'true', SPACE(LENGTH('true')-1)))
AS Cnt_True,
CHAR_LENGTH(js) - CHAR_LENGTH(REPLACE(js, 'false', SPACE(LENGTH('false')-1)))
AS Cnt_False
FROM
( SELECT *, JSON_EXTRACT(jsdata, '$.*') AS js
FROM tab ) t
Demo