refactor: replace Biome with oxlint + oxfmt

Migrate the entire monorepo from Biome 2.4.7 to oxlint 1.56.0 (linter)
and oxfmt 0.41.0 (formatter) for faster lint/format and broader rule
coverage.

- Add `.oxlintrc.json` with React, TypeScript, unicorn, import plugins
  and correctness/suspicious categories
- Add `.oxfmtrc.json` with 2-space indent, import sorting, and Tailwind
  class sorting (all 30+ custom className attributes migrated)
- Add `docs/.oxlintrc.json` and `docs/.oxfmtrc.json` with Next.js plugin
- Update all 12 workspace package.json scripts: `oxlint`, `oxfmt`,
  `oxfmt --check`
- Add `format:check` turbo task and CI step
- Update VS Code settings/extensions to use `oxc.oxc-vscode`
- Update CI path triggers from `biome.json` to new config files
- Remove all `biome-ignore` comments and fix shadowed variables
- Delete `biome.json` and `docs/biome.json`
- Reformat entire codebase with oxfmt

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

docs/public/openapi.json

@@ -4190,13 +4190,24 @@
                           "type": "string",
                           "default": "TMDB API key is not configured"
                         },
-                        "data": {}
+                        "data": {
+                          "type": "object",
+                          "properties": {
+                            "code": {
+                              "const": "TMDB_NOT_CONFIGURED"
+                            }
+                          },
+                          "required": [
+                            "code"
+                          ]
+                        }
                       },
                       "required": [
                         "defined",
                         "code",
                         "status",
-                        "message"
+                        "message",
+                        "data"
                       ]
                     },
                     {