Tested using Arduino IDE 1.8.19 on Windows 10.
with this sketch

// Uno test for monitor copy/paste on Windows10
void setup() {
  Serial.begin(9600);
  Serial.println("Line 1");
  Serial.println("Line 2");
}
void loop() {
}

With AutoScroll OFF or ON
Ctrl+A (shows both lines highlighted) followed by Ctrl+C and then Ctrl+V into notepad => no text

With AutoScroll OFF or ON
Click and drag over both lines (showing both lines highlighted)
followed by Ctrl+C and then Ctrl+V into notepad => no text

With AutoScroll OFF or ON
Click and drag over both lines BUT NOT the first char of the first line
followed by Ctrl+C and then Ctrl+V into notepad =>

ine 1
Line 2