feat: let users change their auto-generated username in Settings

Usernames are auto-assigned at signup (shipped earlier this session)
but there was still no way to change one. Adds a Username field to
Settings, validated client- and server-side against the same
3-20-char lowercase/digits/underscore pattern used for generation,
with a 409 on collision (excluding the user's own current username).

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

apps/web/lib/changelog.ts

@@ -1,5 +1,5 @@
 // Mirrors CHANGELOG.md at the repo root — update both together.
-export const APP_VERSION = "0.13.1";
+export const APP_VERSION = "0.14.0";
 
 export type ChangelogEntry = {
   version: string;
@@ -11,6 +11,13 @@ export type ChangelogEntry = {
 };
 
 export const CHANGELOG: ChangelogEntry[] = [
+  {
+    version: "0.14.0",
+    date: "2026-07-13 21:47",
+    added: [
+      "**Change your username** in Settings — previously auto-assigned at signup with no way to change it.",
+    ],
+  },
   {
     version: "0.13.1",
     date: "2026-07-13 17:25",