I understand that you're writing a character who overcomes their anxiety in heroic ways, and so you want to have a better understanding of what such a person would be like. In light of that, I have 5 recommendations: 1 research article + 4 books.
I recommend you read them in the order provided.
A Humane Vision of Clinical Psychology, <strong>Volume 1</strong> & <strong>Volume 2</strong>
This doesn't directly deal with anxiety (but there's an example case in Vol. 2 that deals with heroism... the father of the patient discussed). Consider this as a pre-requisite for the remaining 4 recommendations, since it deals with what it means to really understand someone at their core. This serves as a "goal" and the information in the rest of the recommendations are checks and balances to help you stay on course.
This book will also help you in getting into the head-space of any character that you wish to write, and then write them in an honest and authentic manner, instead of (unknowingly) relying on cliches.
There are sections of this book that deal with the limits of knowledge. Since this is a book aimed at students pursuing one of the social sciences, in those sections it primarily deals with the limits of scientific knowledge, but the same ideas apply to all forms of knowledge.
<strong>The Hero Transformed by Chana Ullman</strong> (A research article)
I recommend this because your character changes from a harmless kitty into a lion, and this article talks about the experience of being a hero. The information in this may help you flesh out the character in interesting ways (i.e. the positive and negative effects of becoming the heroic lion).
<strong>Phenomenology of Anxiety</strong>
Phenomenology is the study of what's it like to be a person with XYZ (in this case, a person with anxiety). This is where the 1st recommendation will really come in handy.
<strong>Changing Emotion With Emotion</strong>
This book could help you with the character development of not just the kitty but their friends as well. It deals with the emotional aspect of change.
But, instead of a therapist bringing about this change (as described in this book), it'd be other characters and circumstances.
<strong>IRT for Anger, Anxiety, and Depression: It's About Broken Hearts, Not Broken Brains</strong>
This book can also help you with character development. It deals with the cognitive (i.e. thoughts; mental justifications; stories about self, others, and the world) aspect of change for someone with anxiety and other co-occurring emotions.
Same as with the previous book, the therapist would be replaced with other characters and circumstances.
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I know I just gave you a LOT to read but, just in case you develop some perfectionist attitude about your story, let me remind you that drafting is a central aspect of story-writing i.e. you don't have to wait until you finish all the books before you start writing. You could start writing it as you read the books, and consider that as your 1st draft. Then, make subsequent revisions as you learn new things.
In case getting access to these resources are burning a hole in your pocket, DM me and I'll send you an e-copy.
So, are you asking this because you want to better understand other people's state of mind?
If you're asking the question in the OP because you want to better understand other people's state of mind (and in doing so understand why other people aren't able to), then I suggest 3 textbooks (don't worry, they aren't incoherently technical). The 1st deals with the present-moment experience, the 3rd deals with the social skills to understand a person, and the 2nd deals with the connection between the two.
I suggest that you read the books in the order provided.
BTW, the 3rd book integrates all the perspectives mentioned by others in this thread.