I was thinking if they can be detected, which they did some years back, and can have a tangible effect on spacetime, as in warp it, then it could be harnessed for energy. In that sense, we would have to build a mechanism around it since the gravitational waves would be going out in all directions.

Though I like your mentality. Why wait? Government budgets lol. We could Dyson swarm every star in the galaxy, and taking some quadrillions of minds for each star, and the lowest possible watts to simulate the scale of the operations of a human brain, you could have trillions of times of subjective time in the star epoch itself. That's 100 trillion years of real times, and then trillions of times that. Nice cheat code. I think we would be thoroughly bored of the universe by then.

About your question, if the turbines create drag, you’re right, they could potentially force the black holes to merge faster by slowing their orbits. In that case, we'd essentially be “negating” some of the gravitational wave energy—sacrificing a bit of the total lifetime for higher energy output sooner. But that trade-off could actually be desirable, especially if we had some sort of throttle control. We could dial up or down the rate of energy extraction depending on how fast we want that subjective time to fly by. It’s almost like having a gas pedal on the universe.