Autohotkey

;  in this case, the computer DOES move the cursor.
min = 5 ;Number of minutes to wait
loop {
    sleep, % min*60*1000
    mousemove, 10, 0, 20, R
    mousemove, -10, 0, 20, R
}

to NOT move the cursor (it should not disrupt my work)
but the teams apps thinks the user is active.

   SetTimer, FakeMe, 1000 ; check once a second
   Return

   FakeMe:
        If A_TimeIdlePhysical > 300000 ; 5 minutes since last REAL user action
            MouseMove,0,0,0,R ; mouse pointer stays in place but sends a mouse event
   Return

it will wake up the screen.

source : https://www.autohotkey.com/board/topic/95131-how-to-simulate-mouse-movements-every-5-minutes-without-actually-moving-them/

the program you posted, has the c# source code available at that link. so it should not be hard to translate at all.
the relevant parts:

https://mousejiggler…ggle/Jiggler.cs

        internal const int INPUT_MOUSE = 0;
        internal const int MOUSEEVENTF_MOVE = 0x0001; 

        public static void Jiggle (int dx, int dy)
        {
            INPUT inp = new INPUT();
            inp.TYPE = Jiggler.INPUT_MOUSE;
            inp.dx = dx;
            inp.dy = dy;
            inp.mouseData = 0;
            inp.dwFlags = Jiggler.MOUSEEVENTF_MOVE;
            inp.time = 0;
            inp.dwExtraInfo = (IntPtr)0;

            if (SendInput(1, ref inp, 28) != 1)
            {
                throw new Win32Exception();
            }
        }

https://mousejiggler…gle/MainForm.cs

        private void jiggleTimer_Tick(object sender, EventArgs e)
        {
            // jiggle
            if (cbZenJiggle.Checked)
            {
                Jiggler.Jiggle(0, 0);
            }
            else
            {
                if (zig)
                {
                    Jiggler.Jiggle(4, 4);
                }

so it looks like the “zen jiggle” only means that it moves the mouse to 0,0 each timer iteration? that seems fairly innocuous.
maybe its the SendInput method of moving the mouse that causes the cursor to “not move” as you claim?
are you certain that this ‘zen jiggle’ feature does not move the mouse to 0,0 location of screen?