docs(naming): rename middleware.md to proxy.md (next 16)

docs/INDEX.md

@@ -44,8 +44,8 @@ _No specs yet._
 | [Bidirectionele async-comms MCP-agent ↔ user](./patterns/claude-question-channel.md) | active | 2026-05-03 |
 | [Entity Dialog](./patterns/dialog.md) | active | 2026-05-03 |
 | [iron-session](./patterns/iron-session.md) | active | 2026-05-03 |
-| [Proxy (route protection)](./patterns/middleware.md) | active | 2026-05-03 |
 | [Prisma Client singleton](./patterns/prisma-client.md) | active | 2026-05-03 |
+| [Proxy (route protection)](./patterns/proxy.md) | active | 2026-05-03 |
 | [QR-pairing via unauth-SSE + pre-auth cookie](./patterns/qr-login.md) | active | 2026-05-03 |
 | [Route Handler (REST API)](./patterns/route-handler.md) | active | 2026-05-03 |
 | [Server Action](./patterns/server-action.md) | active | 2026-05-03 |

docs/plans/docs-restructure-pbi-spec.md

@@ -256,7 +256,7 @@ pbi:
       acceptance_criteria: |
         - No file under docs/ starts with ``.
         - No file under docs/ uses UPPER, snake_case, or contains spaces.
-        - docs/patterns/middleware.md is renamed to docs/patterns/proxy.md.
+        - docs/patterns/proxy.md is renamed to docs/patterns/proxy.md.
         - Every internal link to renamed files is updated in the same
           commit as the rename.
         - `npm run docs:index` runs cleanly with no missing files.
@@ -308,9 +308,9 @@ pbi:
         - title: "Rename middleware.md → proxy.md"
           description: "Next.js 16 renamed middleware.ts to proxy.ts."
           implementation_plan: |
-            git mv docs/patterns/middleware.md docs/patterns/proxy.md
-            grep -rln "patterns/middleware" docs/ CLAUDE.md AGENTS.md README.md \
-              | xargs sed -i '' 's|patterns/middleware|patterns/proxy|g'
+            git mv docs/patterns/proxy.md docs/patterns/proxy.md
+            grep -rln "patterns/proxy" docs/ CLAUDE.md AGENTS.md README.md \
+              | xargs sed -i '' 's|patterns/proxy|patterns/proxy|g'
             npm run docs:index
             commit: docs(naming): rename middleware.md to proxy.md (next 16)
           priority: 3