[AIC-3343] Apply prompt sync plans

[ctawiah]

Context

This completes the conflict-free local-to-server prompt sync path after durable planning. It supports both the normal plan-review-apply workflow and applying an existing durable plan directly.

Summary

• Plans every project, renders the complete review, blocks resource errors and unresolved server changes or conflicts, confirms once, and applies each project plan.
• Adds --yes for explicit non-interactive plan-then-apply execution while requiring terminal input and output for interactive confirmation.
• Adds --apply <plan-id> to apply without replanning, with one-project workspace inference and explicit --project enforcement when needed.
• Adds typed apply API requests, terminal and partial outcomes, and structured JSON containing plan and apply results.
• Replaces raw plaintext diff JSON with deterministic wide side-by-side panels and narrow or Markdown stacked before-and-after sections.

Verification

• go test ./internal/sync/... ./cmd/sync -count=1
• git diff --check