setCustomValidity() and reportValidity() methods can be used for dynamic Field required and error message in Salesforce Lightning Web Component.

Sample Code:

HTML:

<template>
    <div class="slds-theme--default slds-p-around_large">
        <lightning-input 
            type="toggle" 
            label="Basic option" 
            name="toggle" 
            onchange={onHandleValueChange}>
        </lightning-input><br/><br/>
        <lightning-input 
            type="text" 
            label="Enter some text" 
            name="text" 
            required={requiredBool}  
            class="inputText">
        </lightning-input>
    </div>  
</template>

JavaScript:

import { LightningElement } from "lwc";

export default class sampleLightningWebComponent extends LightningElement {

    requiredBool = false;

    onHandleValueChange( event ) {

        let selectedValue = event.detail.checked;
        console.log( 
            "Event is",
            JSON.stringify( 
                event.detail 
            ) 
        );
        console.log( 
            "Selected Value is",
            selectedValue 
        );
        let inputText = this.template.querySelector( 
            ".inputText" 
        );

        if ( selectedValue === true ) {

            this.requiredBool = true;

            if ( !inputText.value ) {
                
                inputText.setCustomValidity( 
                    "This field is required/mandatory" 
                );
                inputText.reportValidity();

            }

        }
        else {

            let tempBool = false;

            if ( !inputText.value ) {
                /* Setting value to Temp to avoid 
                Value Missing error message */
                inputText.value = "Temp";
                tempBool = true;
            }

            inputText.setCustomValidity( '' );
            inputText.reportValidity();
            this.requiredBool = false;

            if ( tempBool ) {

                inputText.value = undefined;

            }

        }

    }

}

js-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>58.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
        <target>lightning__Tab</target>
    </targets>
</LightningComponentBundle>

Output: