mouse turning is over sensitive and the game needs to bind the mouse cursor and hide it if using it for turning on the overworld.
no sound effects, especially missing for the clicking menu options. also, the sensitivity for the mouse turning is way too high. also, controls need an exit game button.
in the puzzle section: I would highly suggest adding the ability to use hotkeys for common actions, especially the end turn button, and moving the various actions into a single space. moving the mouse all over the screen every single turn gives the feeling of repeating a lot of mouse movement for little reason.
menu buttons could use customized looks
the grass planes look good for the background far away, but everywhere close to where the character and the puzzles are, you can see through them to the ground below giving the ground a splotchy and uneven look to the whole ground, would suggest adding a tileable grass texture to make it not as noticeable.
controls in the puzzle section where the skeleton king you are moving as suddenly cannot do anything is a little confusing. The push button also does not interact with the rock, only the skeleton king, if this is intended it needs more visual representation. Since the skeleton king cannot move, I might suggest making him unselectable unless there are different actions you plan on having him be able to do in the puzzle. Having a character that is selectable when they can do nothing can be confusing.
When finishing the first puzzle, if you walk back into the previous area and hit the button again, the gate respawns, locking you out of continuing. I would suggest spawning the king on the other side of the gate and closing the gate to prevent walking back. Or disabling the pressure plate.
The skeleton king itself looks really good though, and the grid movement in the puzzle works very well!
I would suggest adding a "beginning" and "ending" tile that marks where a puzzle begins, and in the puzzle, where you need to get a unit to win. Suddenly shifting to the puzzle without it is a little jarring.