You can accomplish this using CAST(0 as BIT)
update TestTable
set jsonData = JSON_MODIFY(jsonData, '$.isActive', CAST(0 as BIT))
If you want to set it to true, it is simply CAST(1 as BIT) instead.
This works because in SQL, a boolean is represented as a BIT, which can only be 0 or 1. In its translation to JSON, it converts a bit of 0 to false, and a bit of 1 to true.