LWC setter is not getting called

Question

LWC setter is not getting called.

<template>
 {message}<br><br>1. getter value: {displayMessage}<br><br>2. setter value: {updatedMessage}
</template>

import { LightningElement, api} from 'lwc';
 
export default class GetterSetter extends LightningElement {
   message;
   updatedMessage ='demo';

   connectedCallback(){
    this.message='2';
   }

   renderedCallback(){
    this.message='3';
   }

   get displayMessage(){
    return this.message;
   }

   set displayMessage(value) {
    this.updatedMessage = value.toUpperCase();
   }
}

I have tried salesforce documentation.