Just a warning, you're likely not going to like what I have to say, but if you suffer though it, you may just understand the why's...
First, I truly question the underlining reasoning of your therapist as you moving out will only assure your lifelong dependence on that person's care. Sadly, most of modern therapists design their care around the client needed continued support! They very rarely work to provide the tools to self-support, ever if they say they are, they are not.
Example: You state that you have lived in apartments before and it was very difficult as you are faced with zero control of the World that surrounds your apartment.You state that you have dealt with both anxieties and PTSD near all your life, which is only exasperated with your historical experiences with apartment life... So, based on that knowledge, why would an honorable therapist recommend your moving into that environment!?!?
Second, You say you have a 'functional' relationship with your parents, but that past issues still haunt you. Sorry, I inserted my read regarding your current home relationship... That said, I'm guessing that you are likely feeling the 'normal' want to live independently of your parents. Note the word 'Normal.' Point is, that is not tied to either your anxieties nor your PTSD. It's just 'Normal.'
It is my hope that your therapist helped clarify that difference with you. But, based on the likely position of the therapist, most likely not or limited at best...
Third, You say that you parents are willing to be of help, likely covering the cost of the apartment and other living costs. This will likely come to wear upon you as you will feel some level of control regarding their monthly expense... Commonly, this will come to feed your anxieties as you come to see near everything they say as controlling you.
And, your therapist likely never brought that up even thou it is a common occurrence. Yes, I may seem like I am slamming your therapist. Well, that is true, because it is so very common in todays World. At every meeting, your therapist should be providing you life handles for you to grab and hold onto when you feel the anxieties build. Likely occasional, but not at the end of every session.
How do you know? Each session should start with a review of the last sessions Life Handles (or like terms) and how they have helped and end the session with new ones that came from this session. If not, Run! You need someone that is going to provide you the Life Support your need, not a life time of support.
Should you move out. Not yet! You need to heal the relationship you have with your parents! You need to work at spotting where the starting points are for your anxieties and find means of controlling them when they are still small, tiny feelings. This will provide you insight as to controlling your anxieties. Part of that Life Handle thing!
It is very hard to come to the understanding that the Past is the Past and that people all have regrets as to what they did, said or didn't say or do in their past. They all wished they had the chance to correct their past, to ask forgiveness. As you may have seen me use this with Parrots, it also works just as good with Humans: When you Change Your Vantage Point, you begin seeing things from another persons position. It is very common with this happens from your position and you begin to work on your needed changes. The other person, will see a change and be open to doing the same.
As a Adult, we come to understand that we make errors all the time, being provided a chance to correct those errors is like lifting a heavy burden from another and at the same time from you.
Well, at this point, you have determined that I'm truly crazy or just a very old man passing along what I have learned from long life. May kindness be your guide!