Currently the serial monitor just displays incremental content (with / wo scrolling).
There is no way to clear the screen from the arduino output in order to get a static screen.
There has been some requirements in the past to include ANSI functionality, but the discussion always stalled...
May I suggest to keep it simple and stupid? Please just provide a simple clear screen byte
(e.g. Serial.write (12); // ASCII Form Feed to clear the screen).
That simple improvement could make static screens and menues doable on the serial monitor.

n.b. IMHO using an external ANSI terminal is not in the philosopy of the Arduino IDE.
That is already something for freaks, needs external software, and the need to release the serial connection upon compiling is a pain.

Additional context

Additional requests

• [Feature] Add CLS, CR, LF Arduino#9679
• https://forum.arduino.cc/t/clear-display-on-serial-monitor/1234624

Related

• Serial Monitor plugin system to be able to add protocols like VT100, VTX, VTnnn, etc. #406
• Proper handling of CR/LF in serial monitor [imported] Arduino#346
• Serial monitor does not honor some characters Arduino#3654
• https://forum.arduino.cc/t/clearing-the-console-new-post/1226247/2