feat(profile)!: replace sidebar and add avatar navigation

Rename the global Sidebar route, UI, assets, analytics, and payment return context to Profile. Add accessible message-avatar navigation and preserve the source character across auth and logout flows.

BREAKING CHANGE: /sidebar has been removed; use /profile instead.

src/lib/analytics/payment_analytics_context.ts

@@ -5,7 +5,7 @@ export type PaymentAnalyticsTriggerReason =
   | "daily_chat_limit"
   | "private_topic_limit"
   | "insufficient_credits"
-  | "sidebar_recharge"
+  | "profile_recharge"
   | "vip_cta"
   | "ad_landing"
   | "manual_recharge"
@@ -16,7 +16,7 @@ export type PaymentAnalyticsEntryPoint =
   | "chat_unlock"
   | "private_album_unlock"
   | "private_room"
-  | "sidebar"
+  | "profile"
   | "chat_offer_banner"
   | "subscription_direct"
   | "tip_page"
@@ -33,7 +33,7 @@ const ENTRY_POINTS = new Set<PaymentAnalyticsEntryPoint>([
   "chat_unlock",
   "private_album_unlock",
   "private_room",
-  "sidebar",
+  "profile",
   "chat_offer_banner",
   "subscription_direct",
   "tip_page",
@@ -45,7 +45,7 @@ const TRIGGER_REASONS = new Set<PaymentAnalyticsTriggerReason>([
   "daily_chat_limit",
   "private_topic_limit",
   "insufficient_credits",
-  "sidebar_recharge",
+  "profile_recharge",
   "vip_cta",
   "ad_landing",
   "manual_recharge",