feat(docs): mount the DocsGPT chat widget

Adds a floating "Ask the docs" bubble to every docs page. docsgpt-react
was already a dependency but nothing imported it, so no widget rendered.

The widget reads window and navigator on mount, so it is lazy-loaded
with ssr: false from a client wrapper. Its light/dark theme follows the
site toggle via next-themes, promoted here from a transitive dependency
to a declared one.

The key comes from NEXT_PUBLIC_DOCSGPT_API_KEY and the host from
NEXT_PUBLIC_DOCSGPT_API_HOST. With no key set the wrapper renders
nothing rather than falling through to the demo key the package defaults
to.

Bumping docsgpt-react to ^0.7.0 also drops a duplicate React. The old
^0.6.3 pin depended on React 18 and npm installed a nested 18.3.1 beside
the app's 19.2.8, which would have thrown an invalid hook call on first
render.

docs/package-lock.json

@@ -7,8 +7,9 @@
       "license": "MIT",
       "dependencies": {
         "@vercel/analytics": "^2.0.1",
-        "docsgpt-react": "^0.6.3",
+        "docsgpt-react": "^0.7.0",
         "next": "^16.3.0",
+        "next-themes": "^0.4.6",
         "nextra": "^4.6.1",
         "nextra-theme-docs": "^4.6.1",
         "react": "^19.2.8",
@@ -311,13 +312,6 @@
         "node": ">=6.9.0"
       }
     },
-    "node_modules/@bpmn-io/snarkdown": {
-      "version": "2.2.0",
-      "resolved": "https://registry.npmjs.org/@bpmn-io/snarkdown/-/snarkdown-2.2.0.tgz",
-      "integrity": "sha512-bVD7FIoaBDZeCJkMRgnBPDeptPlto87wt2qaCjf5t8iLaevDmTPaREd6FpBEGsHlUdHFFZWRk4qAoEC5So2M0Q==",
-      "deprecated": "Package no longer supported. Contact Support at https://www.npmjs.com/support for more info.",
-      "license": "MIT"
-    },
     "node_modules/@braintree/sanitize-url": {
       "version": "7.1.2",
       "resolved": "https://registry.npmjs.org/@braintree/sanitize-url/-/sanitize-url-7.1.2.tgz",
@@ -4389,13 +4383,12 @@
       }
     },
     "node_modules/docsgpt-react": {
-      "version": "0.6.3",
-      "resolved": "https://registry.npmjs.org/docsgpt-react/-/docsgpt-react-0.6.3.tgz",
-      "integrity": "sha512-sG2sb129O76ux2KbQJLEJ/rD1CCaO3vAKC4fN8/Ks5GaATC9lbavZy/PH75Y/q0bOMsPkh/Kdq6xSfGTfTIAuA==",
+      "version": "0.7.0",
+      "resolved": "https://registry.npmjs.org/docsgpt-react/-/docsgpt-react-0.7.0.tgz",
+      "integrity": "sha512-/noRUe3+5pudINS+nGYq4aN5NwNI9LC+teU8g23r8QxKubk8/xybFt6HS0ZK9JnCnMC/2GbnNL4kSP0IGw0vaA==",
       "license": "Apache-2.0",
       "dependencies": {
         "@babel/plugin-transform-flow-strip-types": "^7.23.3",
-        "@bpmn-io/snarkdown": "^2.2.0",
         "@parcel/resolver-glob": "^2.16.4",
         "@parcel/transformer-svg-react": "^2.16.4",
         "@parcel/transformer-typescript-tsc": "^2.16.4",
@@ -4404,47 +4397,13 @@
         "class-variance-authority": "^0.7.0",
         "clsx": "^2.1.0",
         "dompurify": "^3.1.5",
-        "flow-bin": "^0.306.0",
+        "flow-bin": "^0.326.0",
         "markdown-it": "^14.1.0",
-        "react": "^18.2.0",
-        "react-dom": "^18.2.0",
+        "react": "^19.2.5",
+        "react-dom": "^19.2.5",
         "styled-components": "^6.1.8"
       }
     },
-    "node_modules/docsgpt-react/node_modules/react": {
-      "version": "18.3.1",
-      "resolved": "https://registry.npmjs.org/react/-/react-18.3.1.tgz",
-      "integrity": "sha512-wS+hAgJShR0KhEvPJArfuPVN1+Hz1t0Y6n5jLrGQbkb4urgPE/0Rve+1kMB1v/oWgHgm4WIcV+i7F2pTVj+2iQ==",
-      "license": "MIT",
-      "dependencies": {
-        "loose-envify": "^1.1.0"
-      },
-      "engines": {
-        "node": ">=0.10.0"
-      }
-    },
-    "node_modules/docsgpt-react/node_modules/react-dom": {
-      "version": "18.3.1",
-      "resolved": "https://registry.npmjs.org/react-dom/-/react-dom-18.3.1.tgz",
-      "integrity": "sha512-5m4nQKp+rZRb09LNH59GM4BxTh9251/ylbKIbpe7TpGxfJ+9kv6BLkLBXIjjspbgbnIBNqlI23tRnTWT0snUIw==",
-      "license": "MIT",
-      "dependencies": {
-        "loose-envify": "^1.1.0",
-        "scheduler": "^0.23.2"
-      },
-      "peerDependencies": {
-        "react": "^18.3.1"
-      }
-    },
-    "node_modules/docsgpt-react/node_modules/scheduler": {
-      "version": "0.23.2",
-      "resolved": "https://registry.npmjs.org/scheduler/-/scheduler-0.23.2.tgz",
-      "integrity": "sha512-UOShsPwz7NrMUqhR6t0hWjFduvOzbtv7toDH1/hIrfRNIDBnnBWd0CwJTGvTpngVlmwGCdP9/Zl/tVrDqcuYzQ==",
-      "license": "MIT",
-      "dependencies": {
-        "loose-envify": "^1.1.0"
-      }
-    },
     "node_modules/dompurify": {
       "version": "3.4.0",
       "resolved": "https://registry.npmjs.org/dompurify/-/dompurify-3.4.0.tgz",
@@ -4765,9 +4724,9 @@
       }
     },
     "node_modules/flow-bin": {
-      "version": "0.306.1",
-      "resolved": "https://registry.npmjs.org/flow-bin/-/flow-bin-0.306.1.tgz",
-      "integrity": "sha512-xcLHE4dGHbsFio7/55YcFgeWttMEvpoC0T9FHj6xDB7frXvi+IQTWuBQtXpWrHPFflaUGF4jpQ1l6Rnlsev+Gw==",
+      "version": "0.326.0",
+      "resolved": "https://registry.npmjs.org/flow-bin/-/flow-bin-0.326.0.tgz",
+      "integrity": "sha512-2WUYp7px5GeXLX+c2iFAUbr7093ta2c7bjox0pVTWaA6guMP91WFq3mkGKKzbKCIjqgDJepmMF5UPLafaJGE/A==",
       "license": "MIT",
       "bin": {
         "flow": "cli.js"
@@ -5544,18 +5503,6 @@
         "url": "https://github.com/sponsors/wooorm"
       }
     },
-    "node_modules/loose-envify": {
-      "version": "1.4.0",
-      "resolved": "https://registry.npmjs.org/loose-envify/-/loose-envify-1.4.0.tgz",
-      "integrity": "sha512-lyuxPGr/Wfhrlem2CL/UcnUc1zcqKAImBDzukY7Y5F/yQiNdko6+fRLevlw1HgMySw7f611UIY408EtxRSoK3Q==",
-      "license": "MIT",
-      "dependencies": {
-        "js-tokens": "^3.0.0 || ^4.0.0"
-      },
-      "bin": {
-        "loose-envify": "cli.js"
-      }
-    },
     "node_modules/lower-case": {
       "version": "2.0.2",
       "resolved": "https://registry.npmjs.org/lower-case/-/lower-case-2.0.2.tgz",