recommender: add Convex to database/backend MCP coverage (#1981)

Picked up from sethconvex's PR #1966 (auto-closed by membership gate),
split off from #1980 (Convex plugin entry refresh) so the editorial
addition to claude-automation-recommender gets its own review.

Changes:

- SKILL.md: add `convex` to the package.json dep-detection grep, update
  the Database row in the indicator table to name Convex, and add a
  Convex MCP row to the MCP recommendation table.

- references/mcp-servers.md: new "Convex MCP" section in the Databases
  group (Supabase / Convex / PostgreSQL / Neon / Turso), and a row in
  the Detection Patterns quick reference.

Convex publishes its MCP server via the `convex` npm package
(`npx convex mcp start`), exposing tables, function-spec, data,
run-once-query, logs, env list/set/get. Same row pattern as the
existing database/backend MCP entries.

Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

plugins/claude-code-setup/skills/claude-automation-recommender/SKILL.md

@@ -39,7 +39,7 @@ ls -la package.json pyproject.toml Cargo.toml go.mod pom.xml 2>/dev/null
 cat package.json 2>/dev/null | head -50
 
 # Check dependencies for MCP server recommendations
-cat package.json 2>/dev/null | grep -E '"(react|vue|angular|next|express|fastapi|django|prisma|supabase|stripe)"'
+cat package.json 2>/dev/null | grep -E '"(react|vue|angular|next|express|fastapi|django|prisma|supabase|convex|stripe)"'
 
 # Check for existing Claude Code config
 ls -la .claude/ CLAUDE.md 2>/dev/null
@@ -55,7 +55,7 @@ ls -la src/ app/ lib/ tests/ components/ pages/ api/ 2>/dev/null
 | Language/Framework | package.json, pyproject.toml, import patterns | Hooks, MCP servers |
 | Frontend stack | React, Vue, Angular, Next.js | Playwright MCP, frontend skills |
 | Backend stack | Express, FastAPI, Django | API documentation tools |
-| Database | Prisma, Supabase, raw SQL | Database MCP servers |
+| Database | Prisma, Supabase, Convex, raw SQL | Database / backend MCP servers |
 | External APIs | Stripe, OpenAI, AWS SDKs | context7 MCP for docs |
 | Testing | Jest, pytest, Playwright configs | Testing hooks, subagents |
 | CI/CD | GitHub Actions, CircleCI | GitHub MCP server |
@@ -75,6 +75,7 @@ See [references/mcp-servers.md](references/mcp-servers.md) for detailed patterns
 | Uses popular libraries (React, Express, etc.) | **context7** - Live documentation lookup |
 | Frontend with UI testing needs | **Playwright** - Browser automation/testing |
 | Uses Supabase | **Supabase MCP** - Direct database operations |
+| Uses Convex | **Convex MCP** - Live deployment introspection, run queries/mutations, manage env vars and logs |
 | PostgreSQL/MySQL database | **Database MCP** - Query and schema tools |
 | GitHub repository | **GitHub MCP** - Issues, PRs, actions |
 | Uses Linear for issues | **Linear MCP** - Issue management |

plugins/claude-code-setup/skills/claude-automation-recommender/references/mcp-servers.md

@@ -72,6 +72,18 @@ MCP (Model Context Protocol) servers extend Claude's capabilities by connecting
 
 **Value**: Claude can query tables, manage auth, and interact with Supabase storage directly.
 
+### Convex MCP
+**Best for**: Projects using Convex as the backend (reactive database + server functions + auth + storage + scheduling, all on one platform)
+
+| Recommend When | Examples |
+|----------------|----------|
+| Convex project detected | `convex` in deps, `convex/` directory present, `convex.json` at repo root |
+| Real-time / reactive UI | `useQuery` / `useMutation` / `useAction` from `convex/react` |
+| Mobile + Convex | `convex/react-native` in deps |
+| AI / chat / agent features on Convex | `@convex-dev/agent` in deps |
+
+**Value**: Claude can introspect the live deployment (tables, function specs, env vars, logs) and execute queries/mutations against it via tools like `tables`, `function-spec`, `data`, `run-once-query`, `logs`, `env list/set/get`. Run via `npx convex mcp start`.
+
 ### PostgreSQL MCP
 **Best for**: Direct PostgreSQL database access
 
@@ -253,6 +265,7 @@ MCP (Model Context Protocol) servers extend Claude's capabilities by connecting
 | Popular npm packages | context7 |
 | React/Vue/Next.js | Playwright MCP |
 | `@supabase/supabase-js` | Supabase MCP |
+| `convex` in deps, `convex/` directory, or `convex.json` | Convex MCP |
 | `pg` or `postgres` | PostgreSQL MCP |
 | GitHub remote | GitHub MCP |
 | `.linear` or Linear refs | Linear MCP |