Yes, Krohnkite on KDE auto-resizes window tiles and keeps the screen full. It's a default setting (monocular view) but can also be turned off.

To use krohnkite you can add it from within KDE - go to Settings > Window Management > KWin Scripts. Then top right select "Get New..." and type K in the search box and it'll be one of the top options.

It works well but you may need to log out and and back in after enabling it to see some of the changes. Also you will probably want to change other KDE panels and layouts to fit how you want to use the desktop in a tiling set up (and there are plenty of widgets available and window animations to add - like Geometry - if you want to a specific tiling set up and look).

KDE is incredibly customisable, but for tiling it may take a little work to get it exactly where you want it. Also worth backing up your settings folders once you've got it how you want it (Konsave for example, or manually)