You can't use in_array outright since it'll only accept a flat array. Just use array_column to get all state values, then make your checking.
Here's the idea:
if (in_array($name, array_column($countries, 'state'))) {
}
Basically, if your $countries are multi leveled, (meaning):
Array
(
    [0] => Array
        (
            [state] => Arizona
            [date] => 2018-01-01
        )
    [1] => Array
        (
            [state] => California
            [date] => 2018-01-01
        )
)
When you apply array_column, you sorta pluck out each state values, then gather them inside an array. It will yield an array like this:
array_column($countries, 'state') ===> Array ( [0] => Arizona [1] => California )
Only then you can use in_array. Just check out the manual, its eloquently stated there very well.