I don’t think I would wait to hear back from Jane for 3 weeks after her birthday and would try to be in touch with Jane on her birthday or soon after to wish her a Happy Birthday.
Regarding her texts. Jane sounds like she may be a teenager given her responses. She is clearly angry that she knows she can’t have what she wants and is using sarcasm as a defense mechanism. I would call Jane as soon as receiving these texts and ask her about her birthday in general. I would allow her to tell me how she feels based on the texts she sent to me and listen to her concerns. I would ask questions based on what she says to determine if there are any other issues or concerns that are not being addressed by the resource family or other providers and then advocate for those identified needs to be met. For example, if she discusses feelings of depression/sadness associated with not being with her parents, and she is not in therapy, I would advocate for her to be seen by a therapist.