For each property in the project (descending into sub-projects), reports the
compatibility status of every enabled_mcp_tools entry against the calling
user's MCP integrations in workspace_id. Also returns an aggregated
integrations_needing_attention list grouping the gaps by integration so
the UI can drive a "configure now" modal in one call.

Used in two contexts that share the same response shape:

• Pre-clone preview — call with a template's id before cloning to
  decide whether to open the warning modal.
• Post-clone status — call with the cloned project's id to render the
  per-property warning chips on the agent page.

project_id may belong to a different workspace than workspace_id (same
cross-workspace rules as project clone), in which case the user must have
read_others on the source project.