[Feature]: Add `specify integration doctor` diagnostic command

[PascalThuet]

Problem Statement

Spec Kit now supports richer integration state: default integration selection,
controlled multi-install, per-integration settings, manifests, shared
infrastructure, and integration-specific command/context directories.

When something looks wrong, users and coding agents still have to infer project
state by manually inspecting files such as .specify/integration.json,
.specify/integrations/*.manifest.json, and generated agent command
directories. This makes it hard to distinguish between:

• an outdated CLI;
• a missing or malformed integration state file;
• a default integration mismatch;
• missing or modified managed files;
• an unsafe multi-install combination;
• stale files left behind after an integration upgrade or switch.

A first-class diagnostic command would make integration issues easier to report,
debug, and safely fix.

Proposed Solution

Add a diagnostic command:

specify integration doctor

The command should inspect the current project and print a concise health report
for integration state.

Example output:

Integration state: OK
Default integration: claude
Installed integrations: claude, codex
Multi-install safe: yes
Shared templates aligned to: claude
Modified managed files: none
Missing managed files: none

For unhealthy state, it should explain the problem and suggest the safest next
command, for example specify integration use <key>,
specify integration upgrade <key>, or specify integration upgrade --force
only when appropriate.

Suggested Checks

• Project contains .specify/ and is a Spec Kit project.
• .specify/integration.json exists and matches the expected schema.
• Default integration is set and is among installed integrations.
• Installed integrations exist in the registry for the running CLI.
• Per-integration settings are readable.
• Manifest files exist for installed integrations where expected.
• Manifest-tracked files are present.
• Manifest-tracked files that changed locally are reported, not overwritten.
• Shared infrastructure manifest is readable where expected.
• Installed integrations are multi-install safe, or unsafe combinations are clearly reported.
• Command/context directories do not have obvious collisions between installed integrations.

JSON Output

A machine-readable form would be useful for coding agents and CI:

specify integration doctor --json

Potential shape:

{
  "status": "ok",
  "default_integration": "claude",
  "installed_integrations": ["claude", "codex"],
  "multi_install_safe": true,
  "findings": []
}

Acceptance Criteria

• specify integration doctor exits 0 for a healthy Spec Kit project.
• It reports the default integration and installed integrations.
• It reports malformed or missing .specify/integration.json without a traceback.
• It reports missing manifest-tracked files.
• It reports modified managed files without changing them.
• It reports unsafe multi-install combinations.
• It gives non-destructive guidance first (use / upgrade before switch / uninstall).
• --json emits stable machine-readable diagnostics.
• Tests cover healthy state, missing state, malformed state, missing files, modified files, and unsafe combinations.

Suggested Tests

pytest tests/integrations/test_integration_subcommand.py tests/integrations/test_manifest.py -v

Context

This is a follow-up to the integration discoverability and multi-install work
tracked around #2498 / #2519 / #2548 / #2549 / #2574. It is separate from the
active specify self upgrade work in #2475.

[PascalThuet]

Quick duplicate check:

I searched for existing issues/PRs around doctor, diagnostic, integration state, integration.json, manifest, and missing/modified managed files.

Related but not duplicate:

• feat: Integration catalog — discovery, versioning, and community distribution #2130 added the integration catalog and integration upgrade
• fix(integration): refresh shared infra on integration switch #2375 fixed shared infra refresh during integration switch
• fix(shared-infra): record skipped files in speckit.manifest.json #2483 fixed manifest recording for skipped shared infra files

Those improve specific install/upgrade paths, but none add a read-only diagnostic command that reports project integration health across state, manifests, missing/modified managed files, multi-install safety, and optional JSON output.

So I think this issue is still useful as a distinct specify integration doctor proposal.