HTML:

<template>
    <div class="slds-box slds-theme--default">
        <lightning-record-edit-form record-id={recordId} object-api-name={objectAPIName} onsuccess={handleSuccess} onsubmit={handleSubmit}>
            <lightning-messages>
            </lightning-messages>
            <lightning-input-address
                address-label="Address"
                street-label="Street"
                city-label="City"
                country-label="Country"
                province-label="State/ Province"
                postal-code-label="Zip/ Postal Code"
                onchange={addressInputChange}
                show-address-lookup>
            </lightning-input-address>
            <lightning-button class="slds-m-top_small" type="submit" label="Update Address">
            </lightning-button>
        </lightning-record-edit-form>
    </div>
</template>

JavaScript:

import { LightningElement,api } from 'lwc';
import { ShowToastEvent } from 'lightning/platformShowToastEvent';

export default class AddressLwc extends LightningElement {
    
    @api recordId;
    @api objectAPIName;
    strStreet;
    strCity;
    strState;
    strCountry;
    strPostalCode;

    handleSuccess( event ) {

        console.log( 'Updated Record Id is ', event.detail.id );
        this.dispatchEvent(
            new ShowToastEvent({
                title: 'Successful Record Update',
                message: 'Record Updated Surccessfully!!!',
                variant: 'success'
            })
        );

    }

    handleSubmit( event ) {
        
        let fields = event.detail.fields;
        console.log( 'Fields are ' +  JSON.stringify( fields ) );
        event.preventDefault(); 

        if ( this.objectAPIName === 'Account' ) {

            fields.BillingStreet = this.strStreet;
            fields.BillingCity = this.strCity;
            fields.BillingState = this.strState;
            fields.BillingCountry = this.strCountry;
            fields.BillingPostalCode = this.strPostalCode;

        } else if ( this.objectAPIName === 'Contact' ) {

            fields.MailingStreet = this.strStreet;
            fields.MailingCity = this.strCity;
            fields.MailingState = this.strState;
            fields.MailingCountry = this.strCountry;
            fields.MailingPostalCode = this.strPostalCode;

        }

        this.template.querySelector( 'lightning-record-edit-form' ).submit( fields );

    }

    addressInputChange( event ) {

        this.strStreet = event.target.street;
        this.strCity =  event.target.city;
        this.strState = event.target.province;
        this.strCountry = event.target.country;
        this.strPostalCode = event.target.postalCode;

    }

}

js-meta.xml:

<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="http://soap.sforce.com/2006/04/metadata">
    <apiVersion>50.0</apiVersion>
    <isExposed>true</isExposed>
    <targets>
        <target>lightning__RecordPage</target>
    </targets>
    <targetConfigs>
        <targetConfig targets="lightning__RecordPage">
            <property name="objectAPIName" type="String" label="Object API Name"/>
        </targetConfig>
    </targetConfigs>
</LightningComponentBundle>

Output: