Fix stuck controller key repeat

[stephenleo]

Summary

• cancel physical controller repeats before the 750 ms routing guard can swallow release events
• clear repeated input through real mode-change, disconnect, picker, shutdown, and exit lifecycle seams
• cap continuous repetition at 3 seconds so missing releases or asynchronous automation failures cannot inject keys indefinitely

Root cause

D-pad repeat started before routing, but release cleanup ran only after routing. A mode transition could activate the held-input guard, swallow the physical release, and leave the 100 ms repeater running system-wide.

Verification

• deterministic red-to-green regression for the swallowed-release sequence
• focused lifecycle wiring and deadman tests
• full typecheck, lint, format check, test suite, build, package check, and diff check
• independent Standards and Spec reviews passed

No release or tag is included.