Transmitting 8 digit ID #

Official Hardware Nano Family Nano 33 BLE
6

I can't confirm this behavior. I can connect, disconnect, and then reconnect.

You may be running into an issue with this which needs the monitor to be open.
while (!Serial);

In this block of code I would add a millis() timer or some delay() so that the values are not sent over and over again in a tight loop. There is probably some message spacing built into the BLE core, but it's best not to spam the central.

while (central.connected()) {
      IDString.writeValue(ID2);
      IDChartest.writeValue(ID);
    }