How to update a column whose value is being calculated from the values exists in other columns of same table in MySql?
One approach:

SELECT @ratio := SUM(averageLikes)/SUM(averageComments)
    FROM User_engagement;
UPDATE User_engagement
    SET totalInteraction = (totalComments + totalLikes) * @ratio;


But that may be impractical...  What happens when anything changes in the table?  Won't you have to recompute and update all the rows in the table?

Instead, do the computation when you need it:

SELECT ue.totalLikes, ue.averageLikes, ue.averageComments,
       (ue.totalComments + ue.totalLikes) * x.ratio AS totalInteraction
    FROM User_engagement AS ue
    JOIN ( SELECT SUM(averageLikes)/SUM(averageComments) as ratio
            FROM User_engagement ) AS x