Nullability mismatch on variable $value and argument value (String / String!)

I believe the error message is trying to tell you that, the type of $column_id and $value is not correct. They should be nullable types just like for $board_id and $item_id.
Try changing this

mutation ($board_id: Int!, $item_id: Int!, $column_id: String, $value: String)

to this

mutation ($board_id: Int!, $item_id: Int!, $column_id: String!, $value: String!)