I am about to accept a position with the federal civil service. I wanted to make certain I received 'credit' for my time at USAFA. I contacted the USAFA Registrars office and they sent me a letter including the following: (it took just a few hours from the request to receipt - they knew exactly what to send me when I mentioned 'Creditable Service')
This will only be a portion of the documentation that you will need. (I didn't qualify for the GI Bill based on the rules at the time). This specifically applies to 'creditable service' when trying to get your military time including time at USNA towards civil service time for benefits such as leave accrual, but it clearly states you qualified as active duty while at USNA.
I wouldn't start with the VA and the trained counselors - great people and well intentioned but it's unlikely they will understand the nuances of your time at USNA. I would speak to someone at the USNA version of Association of Graduates (AOG). They frequently help people like you find jobs/opportunities and have more than likely dealt with someone in your situation quite recently. (My daughter's date to the Ring Dance was separated with diabetes at the end of his 3rd year - she's unavailable to get me his information for the foreseeable future, but if you message me, I can try to help you get contact information of others that have been in your shoes)
There was a post (not sure if it was USNA or some other academy) about someone who voluntarily left and qualified for certain benefits. Can't help you with best way to search for it.
Quite a few universities also have special offices for veterans and they may be able to assist you.
If you have a good Congressional Representative/Senator - they should have a staffer that deals only with Veteran constituents. Though, I have reached out to my Congressman/woman 3 times on a special program and the only response I ever got was how to donate to their re-election efforts.
I had a classmate diagnosed with a terminal illness prior to graduation. He was allowed to graduate and the AOG along with the senior leadership at USAFA when to great efforts to make certain he was gainfully employed.
The VA will definitely know the right steps to get you access to VA specific programs. I use the DAV as my representative for service connected disabilities. They are wonderful, but as stated - service academy people are nuanced in what they do/don't qualify for while at the service academy.
And Captain MJ is definitely correct about State VA offices. Many states have great programs available to veterans and they are frequently under-utilized.
Don't be afraid to ask for help. You will find veterans and specifically the AOG is eager to help. It's our responsibility and it's rewarding.