Guidance on getting desired SQL results

You would start with the query you have, then use that as an intermediate result to get the averages per airline, and then rank the airplanes by how much their empty seat count deviates from their airline's average. For that ranking you can use ROW_NUMBER() and a windowing clause (OVER). Finally, select the rows in that result that are ranked first.

For this chain of building upon previous results, it is handy to use the WITH syntax:

WITH base as (
    SELECT
        a.airplane_id,
        a.airline_id,
        a.total_seats - SUM(b.booked) AS empty_seats
    FROM
        airlines_detail a
    LEFT JOIN bookings b
        ON
            a.airplane_id = b.airplane_id
    GROUP BY  
        a.airplane_id,
        a.airline_id
), average as (
    SELECT
        airline_id,
        AVG(empty_seats) avg_empty_seats
    FROM
        base
    GROUP BY
        airline_id
), ranked as (
    SELECT
        b.airplane_id,
        b.airline_id,
        ROW_NUMBER() OVER (
            PARTITION BY b.airline_id 
            ORDER BY ABS(b.empty_seats - a.avg_empty_seats)
        ) rn
    FROM
        base b
    INNER JOIN average a
        ON
            a.airline_id = b.airline_id
)
SELECT
    airline_id,
    airplane_id
FROM
    ranked
WHERE
    rn = 1;