Apologies ahead of time. This is likely to sound a bit harsh, but please realize that I really, really think you have a lot to offer any company that hires you. You’re passionate, knowledgable, and clearly focused on delivering excellent UX.
Your cover letter does not do you justice and needs revision to show off your skills.
I made some suggestions on your Google doc. I’ll answer your questions here in just a moment, but I wanted to point out two big things about your cover letter that may affect how you go about writing one.
First, your cover letter is about what you can do for a company, not what they can do for you. I agree that it’s great that the internship is an entrance into the industry for you, but the company ultimately doesn’t care. Focus your cover letter on what you can do for them. Take specific job skills from the posting and talk about your knowledge and experience with each.
Most importantly, your cover letter tells no narrative about what makes you stand out. Why should they pick you? Your cover letter is your sales pitch. Like it or not, you are selling your time and talents. Tell them why they should pick you.
To answer your questions:
What do you like and not like about how I talk about my work experience? What’s lacking here is why this experience is related to the posting. Relate back what you’ve done to what the posting requires. It should be apparent without reading the posting how your experience relates to the proposed position. It isn’t for me right now.
Is what I wrote here what you would find relevant to the purpose of a cover letter? No. There’s too much about your goals, and not enough about what you can do for them. Shift your focus.
What content is extra here? The “strongest UX traits” feels misplaced. How do these relate to the job posting?
What did I leave out? I’m not sure at this point. Take another go at it, and it may become more clear.
Being a good UX professional is as much about learning to give and get constructive criticism - an exercise which, often, isn’t fun for either party. Apologies if that was the case for you here. I hope you know that I only give my advice from a place of trying to help, that it is sincere, and - most importantly - I 100% believe in you and your skills. I want you to shine your brightest, and I know a better cover letter will help you get there.
I really hope this helps. If you’d like to give your letter another go, please feel free to tag me and I’d be happy to give it another look.