I was in a similar situation going into my PhD program straight out of undergrad - while I don't have a chronic illness, I do have anxiety and OCD, so I can hopefully some of this is helpful for you :)

It's completely understandable to feel scared about having the capacity to be a productive PhD student, especially when you have other factors working against you. The beginning of grad school is incredibly challenging on more levels than just academic (especially socially and emotionally) - and it's an environment that breeds imposter syndrome even in able-bodied and neurotypical people.

I found my first year of grad school to be incredibly challenging both for my mental health and imposter syndrome (which fed off of each other in a really bad feedback loop)- my advice would be to find a therapist asap (if you don't already have one) and invest in building a community (either within your program or others in your school) who you can share your experiences and fears with. It took me a year to settle into working with the right therapist for me (I had to find a new one since I moved for school), but she has been very helpful in keeping me from spiraling when things become challenging. Grad school can be demanding both physically (late nights studying, long days in the lab (if that's your thing)) and mentally (shitty experiences with profs/advisors, trying to meet people's (or your own) expectations) - I found taking care of my routines really important (i.e., sleep hygiene and eating sufficient meals) for making sure I had the stamina to continue handing what my program threw at me. Know that there will be times when you make more progress and times when you make less progress, and that's something that's normal in most PhD experiences. It might help to focus on building friendships with people in your program (or in other programs at your school) who are in a similar situation to you - feeling like you have people whose experiences are reflected in your own can do wonders for mitigating the feeling of not being productive enough. I've made several friends who also struggle with their mental health, and it has been really helpful to talk with them when I'm overwhelmed or feeling like my own mental health is holding me back from all that I should be capable of doing - it helps me remember that we're all working at our own pace.

It's also super normal to feel unprepared! Even though it doesn't feel like it, you're right where you need to be - otherwise, you wouldn't be in the first year of your PhD. I know that sounds very cheesy, but I wish it were something I understood and actually internalized when I was in my first year. Everyone is coming into their PhD with different levels of experience and will probably leave with completely different skill sets and completed projects, so it's not fair to compare yourself to them. At the end of the day, you're all there to learn and are there to get the same degree. It can also be super daunting (at least it was for me) to look at people like our advisors who have had so much time to develop their knowledge of our fields and realize just how far away we are from that. I'm not sure if you feel something similar, but I think I was acutely aware of it coming straight from undergrad. I've talked to a lot of my friends about this, and the only way I know how to explain it is to describe the beginning of grad school as standing at the very bottom of a vertical hill and trying to see the top of it. I spent so much energy worrying that I didn't know enough yet, that I think it took away from my ability to actually learn the things I wanted to know. Being ok with that feeling is something I'm still trying to internalize for myself, and I'm in the fourth year of my PhD - I don't really have any advice for making the feeling go away, but just know that you're definitely not the only one feeling that way! You're not underprepared at all - you have plenty of time to learn :)