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High turnout always benefiting the Democrats is an old wife’s tale which I have proved here before. Here you go again. I limit this to just the midterms since that is what we have this year.

Midterm House elections. The average turnout for midterms is 40%
2018 50% high, Democrats gained 44 seats
2014 38% low, Republicans gained 8 seats
2010 42% high, Republicans gained 63 seats
2006 38% low, Democrats gained 33 seats
2002 40% average, Republicans gained 8 seats
1998 37% low, Democrats gained 3 seats
1994 42% high, Republicans gained 54 seats
1990 38% low, Democrats gained 7 seats
1986 38% low, democrats gained 5 seats
1982 43% high, democrats gained 27 seats
1978 39% low, Republicans gained 7 seats
1974 39% low, Democrats gained 39 seats
1970 48% high, Democrats gained 12 seats
1966 47% high, Republicans gained 47 seats
1962 46% high, republicans gained 4 seats

When the house changed hands, control 1994, 2010 and 2018, turnout was high. 2 for the Republicans, 1 for the Democrats. But in 2006 when the democrats took control of the house with a net gain of 33 seats, turnout was low. Finally, looked back at gains of one party or the other of 30 or more seats to compare that to voter turnout in the midterms.

2018 50% high, Democrats gained 44 seats
2010 42% high, Republicans gained 63 seats
2006 38% low, Democrats gained 33 seats
1994 42% high, Republicans gained 54 seats
1974 39% low, Democrats gained 39 seats
1966 47% high, Republicans gained 47 seats

In 3 of the 4 high voter turnout midterm elections, it was the republicans who gained 30 or more seats vs. 1 for the Democrats. The two elections that had low voter turnout, the democrats picked up 30 plus seats in both of those.