Sample Code:

HTML:

<template>
    <lightning-card>
        <lightning-input-rich-text>
            <lightning-rich-text-toolbar-button-group
                slot="toolbar"
                aria-label="Sample Button Group">
                <lightning-rich-text-toolbar-button
                    icon-name="utility:save"
                    icon-alternative-text="Save"
                    onclick={handleSave}>
                </lightning-rich-text-toolbar-button>
                <lightning-rich-text-toolbar-button
                    icon-name="utility:email"
                    icon-alternative-text="Email"
                    onclick={handleEmail}>
                </lightning-rich-text-toolbar-button>
            </lightning-rich-text-toolbar-button-group>
        </lightning-input-rich-text>
    </lightning-card>
</template>

JavaScript:

import { LightningElement } from 'lwc';

export default class SampleLWC extends LightningElement {
    
    handleSave() {

        console.log( 'Inside Save' );

    }
    
    handleEmail() {

        console.log( 'Inside Email' );

    }

}

JS-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>55.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
        <target>lightning__Tab</target>
    </targets>
</LightningComponentBundle>

Output: