Hello. Unfounded means that something is not backed up with facts; the thing or claim has no truth in it. So the sentence means that she started realizing that the things she was feeling had some valid reasoning behind them; or that she had every reason to feel scared and anxious.

Unfounded = baseless, unproven, unsupported. An unfounded fear is one that has no basis; it may be irrational. In your sentence, she started realizing that her anxiety and fears were NOT unfounded, which means that there IS a reason for her to be anxious and fearful. I hope this helps!

It's like to say that she started to notice, that her anxiety and fears were incorrect, she made a mistake, there was no bases on what she thought to produce those thoughts earlier. You are welcome.