Keyboard and Mouse inputs are not being registered on Steam Deck

You need to run the game from the desktop, and should then be able to change the controller to mouse and keyboard in the settings.  However it will change back every time the game loads.  You can fix this once and for all by right clicking on the Don't Starve Together entry in Steam, selecting "Properties" and then pasting the following content into "Launch Options":

SteamDeck=0 %command%

When you next load the game it will ask you if you want to use a controller, to which you say no, and after that it should default to the mouse and keyboard.  It also allows you to change the resolution and set the game to full screen, which you can't normally do on the Steam Deck's desktop.