After reviewing nearly every sprint in your workout, well zoomed in, I see a max of 2 seconds offset from the green instruction change to the point the yellow power meets or exceeds the blue target.
Importantly, the yellow actual power line is only 1 second offset from the blue target. I just don’t see that as “very laggy”. It seems reasonably quick to me.
As I see in my intervals, you are getting the full benefit of time at or above the power target. I don’t see a problem here. We are looking at a very narrow window of time.
If you want better control, you may be best to swap to Resistance mode to have full control of the process.