Introduces DateService for time zone handling

Adds DateService using date-fns-tz for robust time zone
conversions and date manipulations.

Refactors DateCalculator and TimeFormatter to utilize the
DateService, centralizing date logic and ensuring consistent
time zone handling throughout the application.

Improves event dragging by updating time displays and data
attributes, handling cross-midnight events correctly.

package-lock.json

@@ -9,6 +9,8 @@
       "version": "1.0.0",
       "dependencies": {
         "@rollup/rollup-win32-x64-msvc": "^4.52.2",
+        "date-fns": "^4.1.0",
+        "date-fns-tz": "^3.2.0",
         "fuse.js": "^7.1.0"
       },
       "devDependencies": {
@@ -1202,6 +1204,25 @@
         "node": ">=20"
       }
     },
+    "node_modules/date-fns": {
+      "version": "4.1.0",
+      "resolved": "https://registry.npmjs.org/date-fns/-/date-fns-4.1.0.tgz",
+      "integrity": "sha512-Ukq0owbQXxa/U3EGtsdVBkR1w7KOQ5gIBqdH2hkvknzZPYvBxb/aa6E8L7tmjFtkwZBu3UXBbjIgPo/Ez4xaNg==",
+      "license": "MIT",
+      "funding": {
+        "type": "github",
+        "url": "https://github.com/sponsors/kossnocorp"
+      }
+    },
+    "node_modules/date-fns-tz": {
+      "version": "3.2.0",
+      "resolved": "https://registry.npmjs.org/date-fns-tz/-/date-fns-tz-3.2.0.tgz",
+      "integrity": "sha512-sg8HqoTEulcbbbVXeg84u5UnlsQa8GS5QXMqjjYIhS4abEVVKIUwe0/l/UhrZdKaL/W5eWZNlbTeEIiOXTcsBQ==",
+      "license": "MIT",
+      "peerDependencies": {
+        "date-fns": "^3.0.0 || ^4.0.0"
+      }
+    },
     "node_modules/debug": {
       "version": "4.4.3",
       "resolved": "https://registry.npmjs.org/debug/-/debug-4.4.3.tgz",