Comment by redacted

In 22H2 it's fully keyboard drivable

  - Win+Z brings up the layout menu
  - number keys select the layout, then where in the chosen layout the current window should go
  - arrow keys then let you select the other windows to complete the tiling

So if I want Firefox (current window) and Slack side by side

  - Win-Z inside FF
  - 1 selects side-by-side
  - 1 again snaps FF to the left (2 would snap to right, and so on for more complex layouts)
  - Slack is the first suggested window (MRU), so Space to snap right

It's not as quick as the mouse interface yet - especially with the mouse improvements MS made - but seems like it could be easily automated with eg Autohotkey