Update homepage, add demos data.

* display ydemo sections dynamically.
* Introduced a new `demos.ts` file for demo content management.
* Added `framer-motion` for animations and updated dependencies in `package.json`.

main-website/package-lock.json

@@ -8,6 +8,7 @@
       "name": "main-website",
       "version": "0.1.0",
       "dependencies": {
+        "framer-motion": "^12.16.0",
         "next": "15.3.3",
         "react": "^19.0.0",
         "react-dom": "^19.0.0"
@@ -3306,6 +3307,33 @@
         "url": "https://github.com/sponsors/ljharb"
       }
     },
+    "node_modules/framer-motion": {
+      "version": "12.16.0",
+      "resolved": "https://registry.npmjs.org/framer-motion/-/framer-motion-12.16.0.tgz",
+      "integrity": "sha512-xryrmD4jSBQrS2IkMdcTmiS4aSKckbS7kLDCuhUn9110SQKG1w3zlq1RTqCblewg+ZYe+m3sdtzQA6cRwo5g8Q==",
+      "license": "MIT",
+      "dependencies": {
+        "motion-dom": "^12.16.0",
+        "motion-utils": "^12.12.1",
+        "tslib": "^2.4.0"
+      },
+      "peerDependencies": {
+        "@emotion/is-prop-valid": "*",
+        "react": "^18.0.0 || ^19.0.0",
+        "react-dom": "^18.0.0 || ^19.0.0"
+      },
+      "peerDependenciesMeta": {
+        "@emotion/is-prop-valid": {
+          "optional": true
+        },
+        "react": {
+          "optional": true
+        },
+        "react-dom": {
+          "optional": true
+        }
+      }
+    },
     "node_modules/function-bind": {
       "version": "1.1.2",
       "resolved": "https://registry.npmjs.org/function-bind/-/function-bind-1.1.2.tgz",
@@ -4578,6 +4606,21 @@
         "url": "https://github.com/sponsors/isaacs"
       }
     },
+    "node_modules/motion-dom": {
+      "version": "12.16.0",
+      "resolved": "https://registry.npmjs.org/motion-dom/-/motion-dom-12.16.0.tgz",
+      "integrity": "sha512-Z2nGwWrrdH4egLEtgYMCEN4V2qQt1qxlKy/uV7w691ztyA41Q5Rbn0KNGbsNVDZr9E8PD2IOQ3hSccRnB6xWzw==",
+      "license": "MIT",
+      "dependencies": {
+        "motion-utils": "^12.12.1"
+      }
+    },
+    "node_modules/motion-utils": {
+      "version": "12.12.1",
+      "resolved": "https://registry.npmjs.org/motion-utils/-/motion-utils-12.12.1.tgz",
+      "integrity": "sha512-f9qiqUHm7hWSLlNW8gS9pisnsN7CRFRD58vNjptKdsqFLpkVnX00TNeD6Q0d27V9KzT7ySFyK1TZ/DShfVOv6w==",
+      "license": "MIT"
+    },
     "node_modules/ms": {
       "version": "2.1.3",
       "resolved": "https://registry.npmjs.org/ms/-/ms-2.1.3.tgz",