Your needs assessment (at least for me) was someone asking questions about how your disability affects you. You will have given medical evidence, so there is no dispute about them believing you. You can't see my disability either, but that didn't matter. They asked what hurts, what symptoms you have and then they will run through things that can help. For me, that was ergonomic equipment, taxi allowance, ability to record lectures and certain computer programs.
The assessment should be made to be very supportive. It is about helping you, you diagnosis is already believed and your evidence should say how it affects you, so that gives them a starting point.
I'm not sure how reimbursement really works. I have it for my taxi allowance, but haven't used it. If you are getting taxis every day, then you book them through a certain company and then student finance sort it out. You pay the public transport cost, for me in London it would be £3 ISH for each taxi journey.
It is completely your choice whether or not to speak to your university. But I would urge you to, you have the evidence, as long as you have a good DDS service, you will be believed. My university gave me access to rest rooms, a personal fire evacuation plan, access to adaptive IT rooms, ability to have easier extensions to assignments (ask my school to take into account that I have already provided evidence) and a note to my lecturers that I may have to leave due to pain and to not draw attention to it.
In your application for DSA, you would have chosen whether to allow the university to access a report. I presume you selected no. Some of the things offered by DSA, will be similar or more easily supported by your university knowing. Also, I know very little about RA, but if it is anything like my chronic pain, there will be days that you cannot come to university/out of the house. Depending on the course you are doing, that may affect attendance requirements. The university could reduce the number you have to attend or say you have to attend seminars but can watch lecture recordings from home. Most DDS support will be invisible (e.g. there is a lot for neurodiveristy or severe allergies etc or invisible mobility issues). It is completely your choice, but unless your DDS is not good, I would communicate with them.