For your first complaint here is what I suggest. Turn off live notifications, then set the notification pull down back to separate, you can select which side you want the quick settings menu to pull down on with the toggle below separate/together after changing to separate. You will have one pull on the preferred side to get to the media player.
If having separate swipe is not an option how about a widget for the media app you are using. I have a 1X4 widget for set up at the top of my home screen for Samsung Music, I have live notifications turned off, I have also turned on control music from the lock screen(Samsung Music app has this) which gives me a full size player while music is playing. Drawback when playing music is that it takes a second swipe to see the lock screen if you vies notifications on there, this of course is only when music is playing. Here is a screenshot of Samsung Music widget on my S24.
The battery icon is unappealing. I was on the Beta for One UI 7 and it was one of my complaints, a few of us complained about this and we also mentioned it was hard to read. The developers made it 10% or 20% larger, didn't do anything for the look though. Hopefully a change will be made for One UI 8.
Swiping down a third time on notification doesn't show all configured controls. Didn't know there was a 3rd page. I do notice if I add every single button to the control panel or whatever that is called then it requires a third pull down but does a person really need every single button on that list added to that box. I don't even use all of them. Maybe try adding the 6 most used ones on the notifications panel, remove those from that control box and then start removing the ones you are not going to use. That box can hold 8 before needing to be swiped down. I would start by removing everyone and then add what you actually are using. Take screen shot can be added to the Edge Panel, but not much else can be. If you feel the need for all of them in that box then you have to resort to an extra swipe to see them all.
