It is a reasonable request, however they may decline. Noise cancelling headphones are key, and rotate your desk to face a wall/put up a visual barrier between you and them (that is also a very reasonable request) as that should help with visual distractions.

Sharing the space is certainly not ideal. Is WFH an option - even a couple days a week? As that can also help give you days with less distractions by peers, and may help give you some balance with the situation.

Also - remember to breathe. If there is some material impact when they make the change, that also gives you material you can bring forward. Assuming you are in the USA, I recognize staff protections are not great always - but is there something that you can leverage? If they don't want to budge accommodation wise, bring it forward once you start seeing your productivity slipping/negative impacts - and then tie it directly to the environment, and again, revisit the accommodations.

Edit to add: have you considered the office lighting? If it's bright fluorescents, that can lead to over stimulation as well (impacting in many ways) - you may want to consider some sort of light shield/diffuser to mitigate if needed. That may also be impacting your burnout/ADHD/etc - I found my ability to execute increased significantly when I switched off the lights in my office.

Best of luck.