game.ts: 1,742 lines against a target of ~300

[cgreening]

src/game/game.ts is 1,742 lines against a stated target of ~300. It is down
from 3,244 and is now the last named size debt in tools/sizes.mjs alongside
npc.ts.

It is no longer the urgent problem it was — the browser shell came out
(engine/shell.ts), so the file is portable and testable, and
test/game.test.ts flies it. This is decomposition for readability now, not to
unblock anything.

Measured by section:

section	lines
header + fields + constructor	690
input	259
mode transitions	161
per-frame	155
combat	115
contracts	104
autopilots	87
HUD	84
world lifecycle	81

Two cuts look real:

1. the input section (259) — key handling and the command dispatch table.
   controls.ts already owns the bindings; this owns execution.
2. the HUD driver (84) — renderHud, updateSight, aimBeams. Pure
   presentation, and hud-binding.ts already owns the frame it paints.

That lands it near 1,300. Getting to ~300 would mean moving the five host
tables and the mode transitions too, and it is worth checking at that point
whether the target is still the right one — the apply* methods ARE the
orchestrator's job, and moving them would scatter the step order.

Caution: the file is 34% prose. The comments carry the step order and the
reasons for it; they should move with the code they explain, not be dropped.