Legally I have to have her in school, we’ve had the Drs reports and absence letters up until now, but their recommendation is to try to get her back to school.
Are you in Germany? In the Bundesland where we live, the cut-off date for the school year literally just changed this academic year. So my 6yo with August birthday is still in Kindergarten (preschool) whereas if he had been born the year previously he would have had to go to school at just-turned-6.
There is generally a very strong feeling here that you should keep children back from starting school for as long as possible unless they are very ready, so the pre-school year classes this year have about 15-25% more kids in them which is a bit of a nightmare for the teachers, especially with staff shortages which seems to be a nationwide (possibly even worldwide??) issue.
Anyway I think in your position, I would see if you can arrange a meeting with the preschool lead and possibly the school, if there's someone there who does this kind of thing, about deferring and putting her back in preschool, because even if you're not in Germany, if the system is anything like Germany, they don't really have a nice gentle easy start in primary - the preschool year of Kindergarten is specifically that, it's tailored to gear them up for school and get them ready. If she's missed that since May of last year, then it's going to be much harder for her.
You could also go back to the doctor and ask them for specific recommendations about how you can get her back to school - can they make a referral for any support?
I feel like it can be so opaque here at times and there is no clear map of what services even exist or who is eligible for them. For example over the last year I've learned all kinds of terms which I had absolutely no idea of previously.
We have been referred to a Fruhförderstelle, which roughly translates as "Early intervention" but I am not sure what to expect from this. (The meeting is on Friday so I can update if you like!) I have been told that they don't do assessment/diagnosis but they can suggest support or advice which can be put into place at home or school/Kindergarten.
The school we are close to has a Förderklasse/support class, which is supposed to be more of a transition class for children having a difficult time adjusting to school. It's still school, but it's more structured like pre-school. I am not sure what happens with this class, whether they stay in it throughout school, transition back into their own year group, transition into the next school year, or what. Because DS seems to be settled in the preschool class (fingers crossed) and we don't have all the info yet about his assessment I haven't looked into this yet, but if it makes sense I think I will try and find out about it. There is a staff member at the school who is the sort of "liason" person who comes around to the Kindergartens and is a contact point for new starters, so I think I can contact her if I have questions.
Then there are 1:1 supports for some kids (Integrationshilfe or Begleitsperson) to help them integrate into mainstream. I have no idea what the criteria is to get these - but some seem to be linked to a charity, whereas others are employed directly by the school (but that was an international school, so £££).
Where there is compulsory schooling, there is also often some kind of legal protection to ensure integration for people with difficulties accessing school in the normal way, usually without the need for a specific diagnosis, or at least a loophole around this (e.g. DS's doctor wrote "social delay" or something like that on one form).
Essentially, if the doctor is saying "Try to get her back to school", then go back and ask what you can/should to to get her back to school and how long for. Then if the suggestions do not work, go back in that time period and explain it is getting worse/still not working.
Keep talking to the school and keep talking to everyone. Keep notes of what has been suggested, what has been tried and the outcome. See if there is a family support group for PANS, either locally or online but specific to that country. It's difficult to read social media posts in your second language, but google translate can pick up a lot of slack for you and it does help to hear from others with relevant experience.
Have you looked at whether the international school has any scholarship places and what the criteria are?
Sorry this took me ages to write so some of it is a bit mixed up as I did go through and read just OP's posts before submitting.