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Although there is somewhat possibility of moving and tiling windows with meta+arrow keys, it is limited.
When window is full screen, and I would press meta+right to tile it to the right, it would not tile the first time I press it, but first stop being maximized, only with second press it would tile. KWin also lacks the possibility of tiling to quarters of screen, not only halves.
I think that it would be better if the windows were tiling at the first keybind press, and if we could also tile them to the quarters of screens.

Kwin does support tiling to quarters when you drag a window to one of the corners, or using one of the Quick Tile Window keyboard shortcuts.
testing in Plasma 4, If I maximize a window and then use one of the Quick Tile Window shortcuts to tile that window to the left/right, it moves immediately. On the other hand if I set the window to Full Screen then the Quick Tile Window shortcuts have no effect (even after hitting the shortcut multiple times). That said, the behavior could have changed in Plasma 5

What Plasma+OS version are you using?

I use the newest Plasma on Arch. Tiling to corners does work when pulling to the corner, but not when using general (left, right, up, down) keybinds. With a maximized window first press of keybind de-maximizes it, only second one tiles it.