Try GNOME extension. Awesome Tile. Number pad arrangement becomes window placement. In settings you can choose gap between window and screen edge. Hitting same key repeatedly resizes that window in its current location.
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Wayland makes it complicated, at least until the tools mature. In X11 one could do a lot, using wmctrl and xdotool. For Wayland Gnome, you might want to look at "Run or raise" and "Window calls" extensions. "Grand theft focus" might be handy too if you are switching apps across workspaces.
In general it sounds like you want 'tiling'. There are multiple window managers that does this, e.g. AwesomeWM, i3, Sway, River etc.
Additionally you typically have 'tiling scripts' that work on top of Gnome and Kwin (Plasma), however unsure what the capabilities are there.
I can atleast speak for Sway:
Here you can can move/select the current focused window relative to whatever key strokes you prefer, the defaults are using Vim-bindings, but arrow keys are also pretty common.
For grabbing a specific window (like in an ordered manner) is probably something that you would need to extend through scripting if the 'basic' movement isn't enough.
Note: A tiling window manager is quite different (in usage) from a stacking one (which is what one is mostly used to) tiling capabilities/scripts
No I don't want tiling, I want windows that can overlap, I just want to control them with hotkeys.
Sway let's you float and overlap windows. Also for both tiled and floating windows you can set the size, position, workspace and monitor by the app id (e.g., firefox) or part of the title (e.g., lemmy).
I still think tiling is ultimately the feature you're looking for, even if it's on a floating DE. Most tiling WMs (Sway included) have the ability to float windows, and can even do so by default while still giving you the keyboard-based workflow that you're after.
Tiling isn't an all or nothing thing, Plasma for example is a floating DE that is capable of tiling in exactly the way you're describing by default