Get posts that match defined arrays of tags

This should be achievable with a taxonomy query, like this:

$query = new WP_Query(
    [
        'tax_query' => [
            'relation' => 'AND',
            [
                'taxonomy' => 'post_tag',
                'terms'    => $platforms,
                'compare'  => 'IN',
            ],
            [
                'taxonomy' => 'post_tag',
                'terms'    => $hashtags,
                'compare'  => 'IN',
            ],
        ],
    ]
);

You just need to substitute the $platforms and $hashtags variables with the appropriate arrays. If there’s a single platform, rather than an array I suggest just using the ID and changing the 'IN' compare value to '=' for the first array.

In my comment I said it would be easier to query with a taxonomy, but I realised that’s not true, the method would be the same as above. It would however make it easier to manage the terms.