<!-- childWebComp.html -->
<template>
    <lightning-button label="Close tab" icon-name="utility:chevronclose" icon-position="right" onclick={handleButtonChange}></lightning-button>
</template>

//  childWebComp.js
import { LightningElement } from 'lwc';

export default class CategoryFilter extends LightningElement {

    handleButtonChange(){
    var close = true;
        const closeclickedevt = new CustomEvent('closeclicked', {
            detail: { close },
        });

         // Fire the custom event
         this.dispatchEvent(closeclickedevt);
    }

}
Now write parent Aura component and controller to changed event

<lightning:card title="AuraDomEventListener" iconName="custom:custom30">
    <aura:set attribute="actions">
        <span class="aura">Aura Component</span>
    </aura:set>
    <div class="slds-m-around_medium">
        <lightning:layout>
            <lightning:layoutItem size="4">
                **<!-- This is an LWC component -->
                <c:childWebComp oncloseclicked="{!c.handleFilterChange}"/>**
            </lightning:layoutItem>
            <lightning:layoutItem size="8" class="slds-p-left_medium">
                {!v.message}
            </lightning:layoutItem>
        </lightning:layout>
    </div>
</lightning:card>



var CloseClicked = event.getParam('close');
    component.set('v.message', 'Close Clicked');


    var workspaceAPI = component.find("workspace");
    workspaceAPI.getFocusedTabInfo().then(function(response) {
        var focusedTabId = response.tabId;
        workspaceAPI.closeTab({tabId: focusedTabId});
    })
    .catch(function(error) {
        console.log(error);
    });
},