Keep a notepad and pencil nearby for brain dumps to take care of later. Other than that, only water bottle for hydration.
It is better to set aside time just to organize before engaging in deep work, because it allows prioritization and helps everything to be right at hand when you are ready.
I select three +/- resources to be available within reach & commit to sticking to those or exchange them with others but try to stick with just about three, to keep from flipping between too many & losing my focus. Ideally those sources stay open on my desk to minimize having to "start over" each time I sit at it to find where I was & pick up where I left off as quickly as possible. I clean up cups & glasses on my breaks. Snail mail is not in immediate view of I want to get stuff done.
I have been taking 10-15 minutes before and after my deep work to tidy up my workspace. During that time I work to clear my tabletop so that all I have in my workspace is my laptop, a notebook and pen, and any relevant materials to what I’m working on.
I always keep my work space super neat and organized so it is that way during deep work too. I find organized spaces extremely soothing and satisfying.
I make sure my desk and room is tidy and I either put a relaxing music on or I work in silance. I also have a glass of water next to me. I switch off sound in my phone not be distracted by any notifications.
It sure isn't easy but you can reach a state of organized workspace/room by moving things slowly out of the way 5-10 minutes a day will clean up your initial mess and will keep your workspace organized!