Combine meta query and give a specific meta query a higher priority

As I already pointed in the comment, all you need to do is change your orderby parameter so that the meta_prio is the first item and followed by the meta_start. So your orderby should look like:

// This array forms an ORDER BY clause with each array item being a column that
// MySQL use when sorting the posts/results.
'orderby' => array(
    // This is the first column, which has the highest priority and sorts by the
    // meta high_prio.
    'meta_prio'  => 'DESC',

    // This is the second column, which sorts by the meta date_start, after MySQL
    // sort the results by the meta high_prio.
    'meta_start' => 'ASC',
)

So with the above example, the generated ORDER BY clause would look something like ORDER BY <meta_prio column> DESC, <meta_start column> ASC and MySQL would first sort the results by the high_prio meta and then sort the sorted results by the date_start meta.

And remember that the array key used in your orderby must match the one in your meta_query, if you’re sorting the results by the meta query clauses in the meta_query array. Additionally, make sure you set the proper type in your meta query clauses; e.g. if the value is a date like 2020-03-12 09:30, then you’d set the type to DATETIME (i.e. 'type' => 'DATETIME'):

'meta_query' => array(
    'relation'   => 'OR',
    'meta_start' => array(
        'key'  => 'date_start',
        'type' => 'DATETIME',
    ),
    'meta_prio'  => array(
        'key'  => 'high_prio',
        'type' => 'NUMERIC',
    )
),
// Make sure the array keys match those in the above meta_query array.
'orderby'    => array(
    'meta_prio'  => 'DESC',
    'meta_start' => 'ASC',
),