Hi Rebekah, I'm sort of new here myself (restarted my shop after not working on it for 2 years). But, I do agree that the Cover Photo takes away from our shops. I noticed a few days ago that I could not see my items when landing on my own page.
I played around and didn't like the empty look without it, so went with the older Banner version. Using the banner allows a visitor to my shop to at least see the top half-ish of my 4 featured items which I hope will draw them in a bit further down the page.
I checked on my phone and the banner (on my shop) doesn't show up, just my logo/avitar (what ever it is called). But on yours, your Cover Photo shows above and behind your logo.
And, all of the items are the same for your shop on the mobile and laptop view; not sure about seeing others items mixed in.
Your cards are adorable by the way! You say that you use all the tags, but perhaps you should change your titles some. I go back and forth with using lots of different titles for one item, but it may help if your titles mirror your tags (most important ones) and your first sentence or two of description.
This item, for example:
https://www.etsy.com/listing/291364339/mix-and-match-set-of-3-greeting-cards?ref=shop_home_active_1You are trying to get buyers who are looking for cards, so I would put those words right at the front of your title "Greeting Cards Set of 3 Mix & Match, Blank Note Cards, Thank You Notes, Digital Print"
That still leaves you with 55 characters and I'm sure you could find more to say about them as you know them better.
Also, you have lovely photography. Just FYI.
One thing I read about Etsy's search engine is that the preference goes to shops with more sales. That sucks for me and others with fewer sales! For my last few sales to friends and family, I have been using the sell in person setting on my phone to increase my sales on Etsy. Just a couple but in may help.
Hope some of this is helpful, and others here are great at giving honest advice!