SheetJS Library can be used in the Salesforce Lightning Web Component to download the record in the Excel format.

1. Go to https://cdn.sheetjs.com/.

2. Select xlsx.full.min.js from the current version. Right click and use Save As option to save the JavaScript as a .js file.

3. The downloaded SheetJS Library JavaScript file should be stored in the Static Resource to reference in the Lightning Web Component.

Sample Lightning Web Component:

HTML:

<template>    
</template>

JavaScript:

import { 
    LightningElement, 
    api, 
    wire 
} from 'lwc';
import SheetJS from '@salesforce/resourceUrl/SheetJSLibrary'; 
import { loadScript } from 'lightning/platformResourceLoader';
import { getRecord } from 'lightning/uiRecordApi';
import { getRelatedListRecords } from 'lightning/uiRelatedListApi';
import { ShowToastEvent } from 'lightning/platformShowToastEvent';

const ACCOUNT_FIELDS = [ 
    'Account.Name', 
    'Account.Industry', 
    'Account.AnnualRevenue' 
];
const CONTACT_FIELDS = [ 
    'Contact.Id', 
    'Contact.Name', 
    'Contact.Email' 
];

export default class ExportToExcel extends LightningElement {

    @api recordId;
    accountName;
    accountIndustry
    accountAnnualRevenue;
    contactRecords;

    @wire( getRecord, { 
        recordId: '$recordId', 
        fields: ACCOUNT_FIELDS } 
    )
    wiredRecord( { 
        error, data  } 
    ) {

        if ( error ) {

            let message = 'Unknown error';
            if ( Array.isArray( error.body ) ) {

                message = error.body.map( e => e.message ).join( ', ' );

            } else if ( typeof error.body.message === 'string' ) {

                message = error.body.message;

            }
            this.dispatchEvent(
                new ShowToastEvent({
                    title: 'Error while fetching Account information',
                    message,
                    variant: 'error',
                }),
            );

        } else if ( data ) {
            
            console.log( 
                'Account is',
                JSON.stringify( data ) 
            );
            this.accountName = data.fields.Name.value;
            this.accountIndustry = data.fields.Industry.value;
            this.accountAnnualRevenue = data.fields.AnnualRevenue.value;

        }
    }

    @wire( 
        getRelatedListRecords, {
        parentRecordId: '$recordId',
        relatedListId: 'Contacts',
        fields: CONTACT_FIELDS
    } )listInfo( { error, data } ) {

        if ( data ) {

            console.log( 
                'Data is', 
                JSON.stringify( data ) 
            );
            let tempRecords = [];

            data.records.forEach( obj => {

                let tempRecord = {};
                tempRecord.Id = obj.fields.Id.value;
                tempRecord.Name = obj.fields.Name.value;
                tempRecord.Email = obj.fields.Email.value;
                tempRecords.push( tempRecord );

            } );

            this.contactRecords = tempRecords;
            console.log( 
                'Records are',
                JSON.stringify( this.contactRecords ) 
            );
            
        } else if ( error ) {
            
            let message = 'Unknown error';
            if ( Array.isArray( error.body ) ) {

                message = error.body.map( e => e.message ).join( ', ' );

            } else if ( typeof error.body.message === 'string' ) {

                message = error.body.message;

            }
            this.dispatchEvent(
                new ShowToastEvent({
                    title: 'Error while fetching Account information',
                    message,
                    variant: 'error',
                }),
            );

        }
    }

    @api async invoke() {
        
        console.log( 'Inside invoke' );
        await loadScript(this, SheetJS); 

        const filename = 'Account - ' + 
            new Date().toLocaleDateString() + 
            '.xlsx';
        const workbook = XLSX.utils.book_new();
        const accountWorksheetData = [];
        const contactWorksheetData = [];

        accountWorksheetData.push( {
            "Name" : this.accountName,
            "Industry" : this.accountIndustry,
            "Annual Revenue" : this.accountAnnualRevenue        
        } );
        const accountWorksheet = XLSX.utils.json_to_sheet(
            accountWorksheetData
        );
        XLSX.utils.book_append_sheet(
            workbook, 
            accountWorksheet, 
            'Account Information'
        );

        const tempContactRecords = this.contactRecords;
        for ( const record of tempContactRecords ) {
            
            console.log(
                'record is',
                JSON.stringify( record )
            );
            contactWorksheetData.push( {
                "Id" : record.Id,
                "Name" : record.Name,
                "Email" : record.Email
               
            } );
        }
        const contactWorksheet = XLSX.utils.json_to_sheet(
            contactWorksheetData
        );
        XLSX.utils.book_append_sheet(
            workbook, 
            contactWorksheet, 
            'Contacts Information'
        );

        console.log(
            'Entering write file'
        );
        const excelBuffer = XLSX.write(
            workbook, 
            { bookType: 'xlsx', type: 'array' }
        );
        const blob = new Blob(
            [excelBuffer], 
            { type: 'application/octet-stream' }
        );

        const a = document.createElement( 'a' );
        a.href = URL.createObjectURL(blob);
        a.download = filename;
        a.click();
        URL.revokeObjectURL(a.href);

    }

}

js-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>61.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
        <target>lightning__RecordAction</target>
        <target>lightning__RecordPage</target>
    </targets>
    <targetConfigs>
        <targetConfig targets="lightning__RecordAction">
            <actionType>Action</actionType>
        </targetConfig>
    </targetConfigs>
</LightningComponentBundle>