How to use UNITY_EXT_LOGGING to turn on timestamps in the player .log file ?

Unity 2022.3.21
Seems

        Environment.SetEnvironmentVariable    ( "UNITY_EXT_LOGGING", "1" );
        Environment.SetEnvironmentVariable    ( "UNITY_EXT_LOGGING", "1", EnvironmentVariableTarget.Process );
        Environment.SetEnvironmentVariable    ( "UNITY_EXT_LOGGING", "1", EnvironmentVariableTarget.User );

have no effect

Are you setting the environment variable before launching the process? It needs to be set on startup. You can also launch the player with the “-timestamps” command line argument.

use this:

public static class DebugTimestamps
{
    [RuntimeInitializeOnLoadMethod(RuntimeInitializeLoadType.BeforeSceneLoad)]
    static void Init()
    {
        Debug.unityLogger.logHandler = new TimestampLogHandler(Debug.unityLogger.logHandler);
    }

    class TimestampLogHandler : ILogHandler
    {
        ILogHandler _default;
        public TimestampLogHandler(ILogHandler def) => _default = def;

        public void LogFormat(LogType type, UnityEngine.Object context, string format, params object[] args)
        {
            _default.LogFormat(type, context, $"[{System.DateTime.Now:MM/dd/yy HH:mm:ss.fff}] {format}", args);
        }

        public void LogException(System.Exception exception, UnityEngine.Object context)
        {
            _default.LogException(exception, context);
        }
    }
}