Receive events

Filter filter = new() { Room = new RoomFilter { Timeline = new RoomEventFilter { Limit = 50, LazyLoadMembers = true } } };
string filterId = await client.CreateFilterAsync(filter);

await foreach (SyncResponse sync in client.SyncLoopAsync(filter: filterId, onRetry: (exception, wait) => Console.Error.WriteLine($"Sync failed, retrying in {wait}: {exception.Message}"), cancellationToken: cancellationToken))
{
    foreach ((string roomId, JoinedRoom room) in sync.Rooms.Join)
    {
        foreach (ClientEvent clientEvent in room.Timeline.Events)
        {
            if (clientEvent.Type != EventTypes.RoomMessage) continue;
            if (!clientEvent.TryGetContent(out MessageContent? message)) continue;
            Console.WriteLine($"[{roomId}] {clientEvent.Sender}: {message.Body}");
        }
    }

    foreach ((string roomId, InvitedRoom invite) in sync.Rooms.Invite)
        Console.WriteLine($"Invited to {roomId}");
}

Store the last NextBatch together with the session and pass it as since to continue where you left off.

When room.Timeline.Limited is true, the server skipped events. Fetch them with GetMessagesAsync starting from room.Timeline.PrevBatch.