refactor: migrate authentication from Supabase to Better Auth and update Prisma schema models

bun.lock

@@ -21,7 +21,6 @@
         "@prisma/adapter-pg": "^7.6.0",
         "@prisma/client": "^7",
         "@repo/api-contract": "workspace:*",
-        "@supabase/supabase-js": "2.101.1",
         "better-auth": "^1.6.4",
         "dotenv": "^17.4.1",
         "hono": "4.12.10",
@@ -54,6 +53,7 @@
         "@tanstack/react-router": "^1.168.10",
         "@tanstack/router-devtools": "^1.166.11",
         "axios": "^1.14.0",
+        "better-auth": "^1.6.4",
         "class-variance-authority": "^0.7.1",
         "clsx": "^2.1.1",
         "date-fns": "^4.1.0",