JSON_MODIFY has 'append' mode that appends value into array.
declare @json nvarchar(4000) = N'{"Id":1,"Name":"Toy Car","Tags":["toy","game"]}'
set @json = JSON_MODIFY(@json, 'append $.Tags', 'sales')
print @json -- Output: {"Id":1,"Name":"Toy Car","Tags":["toy","game","sales"]}
If array on the specified path does not exists, JSON_MODIFY(append) will create new array with a single element:
declare @json nvarchar(4000) = N'{"Id":1,"Name":"Toy Car","Price":34.99}'
set @json = JSON_MODIFY(@json, 'append $.Tags', 'sales')
print @json -- Output {"Id":1,"Name":"Toy Car","Tags":["sales"]}