feat(sidebar): the avatar opens the account menu on every page (S2)

Off / the footer was a plain link home. It is now the same Menu.Root
everywhere; off / its dialog entries link to /?account=<dialog>, which
Home opens once its account is ready and drops from the URL.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01N4f2nya58RoRu4yEmJgRGE

frontend/src/lib/account-dialog-intent.ts

@@ -0,0 +1,33 @@
+/**
+ * The account menu on every page (TASK-self-edit-avatar-menu-20260928 S2).
+ *
+ * The account dialogs live on `/`. Off `/`, the same menu's dialog entries
+ * are links to `/?account=<dialog>`; Home opens that dialog once its account
+ * is ready and drops the parameter, so a reload or Back never opens it again.
+ * Theme needs no dialog and applies where the reader is.
+ *
+ * No dependencies: this ships with the shared sidebar.
+ */
+
+export const ACCOUNT_DIALOG_QUERY_KEY = "account";
+export const ACCOUNT_DIALOG_INTENTS = ["profile", "general", "billing", "logout"] as const;
+export type AccountDialogIntent = (typeof ACCOUNT_DIALOG_INTENTS)[number];
+
+export function accountDialogHref(dialog: AccountDialogIntent): string {
+  return `/?${ACCOUNT_DIALOG_QUERY_KEY}=${dialog}`;
+}
+
+/** The dialog the URL asks for; null when absent or not one of the four. */
+export function parseAccountDialogIntent(search: string): AccountDialogIntent | null {
+  const params = new URLSearchParams(search.startsWith("?") ? search.slice(1) : search);
+  const value = params.get(ACCOUNT_DIALOG_QUERY_KEY);
+  return (ACCOUNT_DIALOG_INTENTS as readonly string[]).includes(value ?? "") ? value as AccountDialogIntent : null;
+}
+
+/** The same query without the account intent (a malformed value is dropped too). */
+export function searchWithoutAccountDialogIntent(search: string): string {
+  const params = new URLSearchParams(search.startsWith("?") ? search.slice(1) : search);
+  params.delete(ACCOUNT_DIALOG_QUERY_KEY);
+  const query = params.toString();
+  return query ? `?${query}` : "";
+}