I'm a Welfare Rights Officer and just rep at tribunals.
First off. Don't pay for help with claiming. There are local services to you who will help FREE of charge. I would suggest: council welfare rights service, unemployed workers centre or Citizens Advice. There will be a facility for telephone support with form filling.
Second - you already have FAB evidence. And that's your ESA tribunal and support group status. Whilst people (including DWP) will try to tell you the two benefits (PIP and the Work Capability Assessment) are different. There is a HUGE amount of cross over. I often use one benefit to help argue points for the other. There's even caselaw on it which will then hammer home the points I've argued. For example the activity of 'Getting About' in the work capability assessment is very similar to activity 11/ planning and following journeys for PIP. Even if you got SG status with no descriptor points - but achieved it via 'substantial risk' - that is super helpful for PIP. So my advice here include and use your ESA tribunal decision notice as part of your evidence.
In terms of medical evidence - yes, it helps. I actually win more tribunals without it than with it. What is more important is how the form is completed and the info that is documented in your medical assessment (this is done via appointment after you've submitted your claim form).
I would think these issues are relevant. But you can adapt to suit.
MEAL PREP
I'm thinking you may not have sufficient motivation to prep and cook a meal from fresh ingredients (most - 50% or more) of the time? This will be as a consequence of poor mental health and perhaps issues with being overwhelmed/ distracted relating to autism.
You are probably looking at points here for prompting.
TAKING NUTRITION
A possibility are you able to eat most days (this includes snacks)? If your depression is so severe and you've lost weight as a consequence, you would have an argument here for needing prompting and encouragement. The bar is high here.
MEDICATION / THERAPY
If you need reminding and encouragement to take your meds - document it. What would happen if you didn't get that encouragement? Are you aware your mental health is dipping and you know to get support - eg call crisis team or do you rely (need) someone else (eg friend/ family) to monitor your mental health?
WASHING / BATHING
Do you need prompting and encouraging to take a daily shower/ bath? Do you go days on end without bathing/ showering?
Therefore prompting needed.
TOILETING
Sorry limited info but I'm assuming that's fine.
DRESSING
Are you motivated to dress/ undress daily, including putting on clean and appropriate clothing? If not - due to poor mental health you would score points here for need for prompting.
COMMUNICATING
Unless you need bilateral hearing aids or have a severe speech impediment, you won't score points here.
READING
Assuming this may be OK, given you're on here. Unless of course you are doing it via speech to text recognition.
ENGAGING
I would be arguing social support here. It's about all types of face to face (not telephone) engagement. So includes family, friends, house mates, neighbours, doctors, any professionals, shop assistants. Etc! You've said you can't manage a GP appointment without someone else! The social support needs to come from someone (they don't have to exist) who will attend most types of engagement with you. They would know you well, so could advocate for you, know what will trigger you, distract you, minimise distress to you.
BUDGETING
Are you too depressed to deal with day to day budgeting? Do you not open post?
PLANNING AND FOLLOWING JOURNEYS
You are needing to demonstrate 'overwhelming psychological distress' here at taking a journey. This may be harder in your case as you say you don't go out at all! If you describe in your form how you shop, attend appointments, how you managed job centre appointments when you had to go. Basically describe any outings you take.
MOVING AROUND
It's about physical ability to walk outside. From what you've said you have no physical health issues. Panic attacks and mental health restrictions are not within scope of this activity.
And bingo. I would think you are looking at enhanced rate daily living and perhaps standard (or no) mobility.
Get your claim in now :-)