[SDK] update state structure (less duplication, one state enum)

- remove media from LocalMembership file

sdk/src/participationState.ts

@@ -0,0 +1,42 @@
+/*
+Copyright 2026 Element Creations Ltd.
+
+SPDX-License-Identifier: AGPL-3.0-only OR LicenseRef-Element-Commercial
+Please see LICENSE in the repository root for full details.
+*/
+
+import { type ParticipationState } from "./api";
+import { toMatrixRTCError } from "./errors";
+import { type MembershipState } from "./matrixrtc/LocalMembership";
+import { MediaConnectionState } from "./media-backend/api";
+
+/**
+ * The membership combined with the local media connection, in priority
+ * order; `left` and `failed` are absorbing. "Connected once" is tracked here
+ * rather than in the membership because `connected` needs both links.
+ */
+export function participationState(
+  previous: ParticipationState,
+  membership: MembershipState,
+  media: MediaConnectionState | Error,
+): ParticipationState {
+  if (membership.kind === "left") return { kind: "left" };
+  if (previous.kind === "failed") return previous;
+  if (membership.kind === "failed") return membership;
+  if (media instanceof Error)
+    return { kind: "failed", error: toMatrixRTCError(media) };
+  if (membership.kind === "waitingForTransport") return membership;
+  if (membership.kind === "joining") return { kind: "connecting" };
+  const reason =
+    membership.kind === "reconnecting"
+      ? membership.reason
+      : media === MediaConnectionState.Connected
+        ? null
+        : "media";
+  if (reason === null) return { kind: "connected" };
+  const wasConnected =
+    previous.kind === "connected" || previous.kind === "reconnecting";
+  return wasConnected
+    ? { kind: "reconnecting", reason }
+    : { kind: "connecting" };
+}