How do I get to this island in the middle of nowhere in the north-east section of the map?
Solution 1:
You can get on this island by gliding. For this, you need to jump from the peak at Starsnatch cliff (on the red circle added to your picture).
In order to get enough stamina, you should increase your rank at the Anemo and Geo statues of the Seven to increase your max stamina. After that, you may use food that reduces stamina consumption during gliding like Barbatos Ratatouille, and during the glide you may use food to regenerate your stamina, like Northern Smoked Chicken