fix(ci): stabilize docker-git checks

[skulidropek]

Summary

• move docker-git terminal cursor recovery to Effect platform services and use typed runtime requirements in SSH flows
• split oversized menu, websocket, and prompt modules so app/lib pass lint, duplicate detection, and Effect-specific rules
• add dist-deps-prune to the main Check workflow and align terminal-focused tests with the verified behavior

Mathematical guarantees

• Invariant: interactive TUI handoff preserves a recoverable terminal state before and after SSH/session attach flows.
• Invariant: terminal repair/restore effects are total at the boundary and do not surface unchecked exceptions to callers.
• Invariant: CI coverage for the release package now includes the dist dependency prune gate in the primary workflow.

Verification

• bun run --cwd packages/app typecheck
• bun run --cwd packages/lib typecheck
• bun run --cwd packages/app lint
• bun run --cwd packages/lib lint
• bun run --cwd packages/app lint:effect
• bun run --cwd packages/lib lint:effect
• bun run --cwd packages/app test
• bun run --cwd packages/lib test
• bun run --cwd packages/api typecheck
• bun run --cwd packages/api lint
• bun run --cwd packages/api test
• bun run --cwd packages/app build
• bun run --cwd packages/api build
• bun run check:dist-deps-prune