lightning/uiRelatedListApi can be used to find number of related records using Lightning Web Component. Check the sample code below:

Sample Code:

HTML:

<template>
    <lightning-card>
        No of Contacts is {recordCount}
    </lightning-card>
</template>

JavaScript:

import { LightningElement, wire, api } from 'lwc';
import { getRelatedListCount } from 'lightning/uiRelatedListApi';

export default class RelatedListComponent extends LightningElement {

    @api recordId;
    recordCount;

    @wire( getRelatedListCount, {

        parentRecordId: '$recordId',
        relatedListId: 'Contacts'

    })listInfo( { error, data } ) {

        if ( data ) {

            console.log( 'Data is ' + JSON.stringify( data ) );
            this.recordCount = data.count;

        } else if ( error ) {
            
            console.log( 'Error occured', JSON.stringify( error ) );

        }

    }

}

js-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>52.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
        <target>lightning__RecordPage</target>
    </targets>
    <targetConfigs>
        <targetConfig targets="lightning__RecordPage">
            <objects>
                <object>Account</object>
            </objects>
        </targetConfig>
    </targetConfigs>
</LightningComponentBundle>

Output: