refactor: Rename agent modes breakdown→plan, decompose→detail

Full rename across the codebase for clarity:
- breakdown (initiative→phases) is now "plan"
- decompose (phase→tasks) is now "detail"

Updates schema enums, TypeScript types, events, prompts, output handler,
tRPC procedures, CLI commands, frontend components, tests, and docs.
Also fixes 0022 migration multi-statement issue (adds statement-breakpoint markers).

docs/agent.md

@@ -9,7 +9,7 @@
 | `types.ts` | Core types: `AgentInfo`, `AgentManager` interface, `SpawnOptions`, `StreamEvent` |
 | `manager.ts` | `MultiProviderAgentManager` — main orchestrator class |
 | `process-manager.ts` | `AgentProcessManager` — worktree creation, command building, detached spawn |
-| `output-handler.ts` | `OutputHandler` — JSONL stream parsing, completion detection, proposal creation |
+| `output-handler.ts` | `OutputHandler` — JSONL stream parsing, completion detection, proposal creation, task dedup |
 | `file-tailer.ts` | `FileTailer` — watches output files, emits line events |
 | `file-io.ts` | Input/output file I/O: frontmatter writing, signal.json reading, tiptap conversion |
 | `markdown-to-tiptap.ts` | Markdown to Tiptap JSON conversion using MarkdownManager |
@@ -24,7 +24,7 @@
 | `accounts/` | Account discovery, config dir setup, credential management, usage API |
 | `credentials/` | `AccountCredentialManager` — credential injection per account |
 | `lifecycle/` | `LifecycleController` — retry policy, signal recovery, missing signal instructions |
-| `prompts/` | Mode-specific prompt builders (execute, discuss, breakdown, decompose, refine) |
+| `prompts/` | Mode-specific prompt builders (execute, discuss, plan, detail, refine) |
 
 ## Key Flows