I have taken 9+ hour flights in the past while on the combo pill. When I started the pill, I didn’t know about the need to walk around the plane (& I’m not sure that I actually did do it that much). I personally experienced no problems back then, but now that I know, I try to walk around the plane to get some circulation going.
I took a 9+ hour flight last week, and went to the bathroom around 3 times. Around halfway through the flight, I also walked a lap around the plane and did some leg exercises at the back (I’m not a doctor and this is my personal experience). I also didn’t use compression socks for my flights, but wearing them is not a bad idea.
As someone who gets anxious very easily, I can tell you I stressed a lot when nothing bad happened. Walk regularly, and enjoy your trip!