fix(presence): Do Not Disturb is real "busy" presence and keeps your status (#283)

DND was sent as presence unavailable with the literal status text
"dnd": it replaced your status, and other clients showed "dnd". Where
the server supports MSC3026 (busy_presence), DND now sends presence
org.matrix.msc3026.busy and leaves the status alone (Synapse keeps
busy across /sync set_presence=online). Busy renders as red "Do Not
Disturb" with the real status line; the legacy unavailable + "dnd"
encoding is still recognised and still used on servers without it.
Status saves / clears no longer downgrade busy. The SDK rejects
non-spec presences, so busy goes through a direct authed PUT.

Fixes #283

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_017PCb59uY3UKqDqt7B6hzd5

src/app/utils/busyPresence.ts

@@ -0,0 +1,21 @@
+/**
+ * [Gitea #283] Do Not Disturb as a real presence state: MSC3026 "busy"
+ * (Synapse `experimental_features.msc3026_enabled`). Before, DND was sent as
+ * presence `unavailable` with the literal status text "dnd", which replaced
+ * your status and showed as "dnd" in other clients.
+ */
+export const BUSY_PRESENCE = 'org.matrix.msc3026.busy';
+export const BUSY_PRESENCE_FEATURE = 'org.matrix.msc3026.busy_presence';
+
+let busySupported = false;
+
+/** Recorded by the presence updater from the server's unstable_features. */
+export const setBusyPresenceSupported = (supported: boolean): void => {
+  busySupported = supported;
+};
+
+export const isBusyPresenceSupported = (): boolean => busySupported;
+
+/** Pure: whether a presence means Do Not Disturb (busy, or the legacy "dnd" text). */
+export const isDndPresence = (presence: string | undefined, status: string | undefined): boolean =>
+  presence === BUSY_PRESENCE || (presence === 'unavailable' && status === 'dnd');