contract(stdio): migrate the stdio MCP server's 102 tools to @loopover/contract — typed handlers, no hand-mirrored shapes

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Context

Part of #9515; the stdio third of what #9518 originally covered, split out so each migration is a single reviewable PR.

packages/loopover-mcp/bin/loopover-mcp.ts registers 102 tools, of which (after #9517's pilot) only a handful declare an outputSchema. Its ~85 shape constants (:371-1104) hand-mirror the remote server's — several say so in their own comments (:376, :381, :407, …) — and the registration helper erases all typing (:1740-1742, three anys), so every handler takes (input: any). STDIO_TOOL_DESCRIPTORS (:1108-1668) is a third hand-maintained list of name/category/description for all 102.

Two divergences #9517 found and modelled as unions, which converge here: loopover_get_repo_context and loopover_get_pr_reviewability return different payloads from this server than from the remote one (this server proxies the REST route; the remote builds its own object). Resolving them is wire-visible and belongs in this issue's batches, not the keystone's.

Requirements

1. Migrate all 102 tools to register from @loopover/contract, by category, reusing the entries contract(remote): migrate the remote MCP server's tools to @loopover/contract — typed handlers, real output schemas #9518 lands for tools that exist on both servers rather than adding a second definition.
2. Typed handlers. The registration helper stops erasing types; handlers derive their input type via z.infer. No (input: any) remains — enforce with a lint/grep gate.
3. Real output schemas on every tool, replacing unschematized structuredContent.
4. Delete STDIO_TOOL_DESCRIPTORS. Name, category, and description come from the registry; the tools CLI command and _meta.category read it.
5. Converge the two divergent payloads with the remote server, so one tool name means one shape. Whichever side changes, the change is wire-visible and gets called out explicitly in the PR body.
6. buildPlanDag/validatePlanDag (:173-215, hand-duplicated from src/services/plan-dag.ts) move to one shared home and the duplicate is deleted.
7. No wire regression otherwise: names, descriptions, and input shapes preserved or widened, asserted by a tools/list snapshot per batch. Full branch-counted coverage.

Non-goals

• The remote (contract(remote): migrate the remote MCP server's tools to @loopover/contract — typed handlers, real output schemas #9518) and miner server migrations.
• The typed API client and CLI-surface generation (contract: generate every derived surface — typed stdio client, CLI from one spec table, tool-reference docs, miner dedup, UI z.infer types #9521) — though this issue's contract entries are what make that possible.

Deliverables

• All 102 tools registered from the contract, handlers typed, any gate in CI
• Real output schemas throughout
• STDIO_TOOL_DESCRIPTORS deleted
• get_repo_context / get_pr_reviewability payloads converged with the remote server
• Plan-DAG duplication eliminated
• Per-batch tools/list snapshots

Expected outcome

grep -rn "mirror of the remote" packages/loopover-mcp returns nothing, no zod shape describing the same contract exists twice in the repo, and a caller gets the same shape from a tool name regardless of which server answered.

References

Part of #9515. Blocked by #9517 and #9518 (shared entries land there first). Split from #9518, alongside the miner server migration. Unblocks #9521.

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JSO-6588