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

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