Welcome to the forum, Brianela.
Your surgeon does indeed need to know about your complicated comorbidities. The EDS might be the big one, although dysautonomia is an umbrella term that covers a lot of problems.
I have some autonomic dysfunctions that cause me to get suddenly overheated and seriously high blood pressure. Mine was caused by a bunch of crushed vertebrae, 2 in my neck. What sort you have will determine if they will have to give you special treatment.
Ehlers-Danlos is important if you have periodontitis or mitral valve prolapse because they will have to give you antibiotics. They will also want some heart tests. I'd had a heart attack, so had to have a stress test even though I had had no heart problems for years.
Take with you as much information, test results, imaging disks, any reports, list of allergies, medications you take.
It's possible, if your conditions are bad, they could refuse you as a patient. No use worrying about it though. You wouldn't have been recommended for this surgery if you didn't need it and obviously couldn't tolerate it.
Best wishes. Keep in touch. We aren't doctors, just patients, but we can sympathize and hopefully reduce your anxiety by caring.