Hi there, sounds like a stressful situation and I'm sorry that this has happened to your family. I had a similar thing happen when I was much younger in that a 'friend' had stolen some of my toys. I still remember feeling so angry and cheated and I was glad that my mum brought it up with the girl's parents.
I think it is fairly clear that the girl has indeed stolen the items. The chances of them simply "going missing" hours after she left the house and her happening to buy the exact same items are almost zero.
I dislike confrontation and can totally understand your reasoning (i.e. being friends with parents, vulnerable child), however, respectfully, I'm not sure that encouraging your daughter to "let it go" is the right approach. I imagine she feels very hurt and powerless here and so this teaches her the wrong message, sadly one that many girls and women already hear in some many areas of life i.e. that we needs to keep quiet and let people take advantage of us in order to "keep the peace". Teaching her how to stand up for herself in an assertive manner will be a valuable lesson that will benefit her across her whole lifetime. Hopefully it will also be a lesson for the girl that has stolen these items that she cannot expect to take things from others without a consequence.
You say that this girl is vulnerable, which I'm assuming implies possible mental health problems/neurodiversity/attachment issues. Is she known for acting impulsively/lying/difficult relationships with others? If so, I would be respectful and mindful of this and acknowledge that she may struggle with socially appropriate behaviours, but definitely not use it as a reason not to say something. She is likely to need more guidance on these issues, not less.
Seeing as you are already friends with the girl's parents, this may actually make things easier as you can gauge how they might respond to things and choose your words/approach carefully. I would meet face to face over coffee and make it clear that you don't want to fall out over this. Make it clear to them that you would not go and accuse their daughter lightly, hence why you have taken several months to say something, but that you have considered all the facts and it seems likely that she has taken the items. Keep it calm and about simply establishing the facts and making sure the items end up with the rightful owner, don't delve too much into emotions or judging/evaluating anyone's behaviour, parents or child.
Ask her/them to provide an explanation of where the items came from and see what happens. If they say they bought them for her, they are either telling the truth or telling an outright lie - in either case, I would drop it. If she/they say that she bought them herself while shopping alone, ask for specifics e.g. shop, price (if you remember the correct info).
Good luck!