@WipersThymes
Check that your new Kindle is selected in your Amazon account otherwise it will still be sending books to your old one when you buy them.
If you're looking in your Kindle to find the newest books you bought, go the library screen and touch the three horizontal lines icon in the top right.
Make sure the view options is on all and the sort by is set to most recent, then you'll see if your new book is there. Also make sure your new Kindle has the wifi on and is connected to your wifi network.
I find that, if my kindle and collections get out of control (I've had a Kindle since they were introduced, have bought over 1000 x 99 p books, that are mostly unread because I'm an enthusiastic participant in the Japanese art of Tsondoku and keep making random collections for various reasons), it's easier to go into the 'manage content and devices' section on the laptop, delete or rename some the unused collections, make new ones etc and also put books in collections in bulk as it's easier to scroll and select. It can be quite a nice thing to do to browse through your purchases for books you may have forgotten buying - many a time I see a book in a bookshop or library, I see someone reading it or it's mentioned by a friend or on a podcast and when I look, I already bought it for 99p some time ago.
Once you've completed your Kindle housekeeping, make sure the wifi on your kindle is on and it should update the collections and covers. Although it doesn't always seem to automatically download the books but it will do it when you try to open it - you can always connect it to the wifi on your phone/wherever you are if you're not at home.