Fix "Next" never sending admin logs for rounds outside the cache, show a round's total logs on the UI (#16531)

* Fix next never sending logs for rounds outside the cache

* Show round's total log count on the ui

* Disable next button when waiting for a next response

* Cleanup AdminLogsEui.CurrentRoundId

* Fix popout window width

Content.Server/Administration/Logs/IAdminLogManager.cs

@@ -23,4 +23,5 @@ public interface IAdminLogManager : ISharedAdminLogManager
     IAsyncEnumerable<string> CurrentRoundMessages(LogFilter? filter = null);
     IAsyncEnumerable<JsonDocument> CurrentRoundJson(LogFilter? filter = null);
     Task<Round> CurrentRound();
+    Task<int> CountLogs(int round);
 }