Nice to hear from you again.
I'm definitely not an expert in this field, but I tried my best to find some information.
According to one website I found, people who have a "Grad der Behinderung"/ GdB of 50+ receive a so-called "Schwerbehindertenausweis" (ID for severely disabled). If you have a GdB of 20, you receive a "Feststellungsbescheid"(certificate stating your disability). A GdB below 20 does not give you either (certificate or ID).
Regarding your question how the form of disability affects your case, I couldn't find a specific answer. However, one source I found states that you should always inform the authorities immediately about your condition, in order to quickly receive the necessary support. The source also advises to visit specialists to get the required medical certificates explaining your condition, so you can submit them at your asylum hearing at BAMF.
BAMF takes this into account and assesses if your disability can endanger your life in your country of origin, for example because you wouldn't have access to the necessary medical treatment. The source eventually mentions that, while physical or cognitive disability doesn't pose a sufficient reason for asylum, it can still protect you from being deported in case of a rejection of your claim.
Here is more information by the Berlin service website on the ID for severely disabled and "types of care": https://www.berlin.de/willkommenszentrum/en/everyday-life/people-with-disabilities/
In Berlin, there is a center called "Berliner Zentrum für Selbstbestimmtes Leben" that is listed as the central point of contact for advice for people with disabilities: http://www.bzsl.de/start.html
It may be best to contact them for more advice on social benefits or a refugee support service in order to find out how your condition affects your case.
I hope this information helps a bit. Please reach out to us again if you need any further assistance or have more questions!
All the best,