refactor(前端): 去掉 nanoid 和 date-fns；「12月」这种时长改说「1年」，年月按东八区日历数

时长拆分（比赛倒计时、比赛时长、主页「最近一次提交」）改用自己写的东八区日历差，
和 zonedParts 同一个口径，不再跟浏览器时区走。顺手删掉几次重设计后已经没人用的
getRandomId、durationFromValue 和 DURATION_OPTIONS / LONG_DURATION_OPTIONS。

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

apps/web/package.json

@@ -31,12 +31,10 @@
     "chartjs-chart-wordcloud": "^4.4.5",
     "codemirror": "^6.0.2",
     "copy-text-to-clipboard": "^3.2.2",
-    "date-fns": "^4.4.0",
     "fflate": "^0.8.3",
     "lib0": "0.2.119",
     "markdown-it": "^14.3.0",
     "naive-ui": "^2.45.3",
-    "nanoid": "^6.0.2",
     "normalize.css": "^8.0.1",
     "pele": "1.6.0",
     "pinia": "^4.0.3",