Not able to create Contact using Sites in Salesforce using LWC

Question

I have created a public Site and given permissions for the guest profile with Create and Read for both Account(Only Read) and Contact. Then I have given OWD as Public Read/Write for Account and Contact.

Created a VF page, App and LWC and added VF to sites getting below error while saving the record.

You do not have the level of access necessary to perform the operation you requested. Please contact the owner of the record or your administrator if access is necessary.

VF Page:

<apex:page showHeader="false" sidebar="false">
    <apex:includeLightning />    
    <div id="LightningComponentid" />    
    <script>
    $Lightning.use("c:publicsites", function() {
        $Lightning.createComponent("c:createContact",
          { 
          },
          "LightningComponentid",
          function(cmp) {
             
          });
    });
    </script>
</apex:page>

App:

<aura:application access="GLOBAL" extends="ltng:outApp" implements="ltng:allowGuestAccess">
    <aura:dependency resource="createContact"/>
</aura:application>

LWC - createContact

<template>
    <lightning-record-edit-form object-api-name="Contact" onsuccess={handleSuccess} onsubmit ={handleSubmit}>
        <lightning-messages>
        </lightning-messages>
        <lightning-input-field field-name='AccountId'></lightning-input-field>
        <lightning-input-field field-name='FirstName'></lightning-input-field>
        <lightning-input-field field-name='LastName'></lightning-input-field>
        <lightning-input-field field-name='Email'></lightning-input-field>
        <lightning-button class="slds-m-top_small" type="submit" label="Create Contact">
        </lightning-button>
    </lightning-record-edit-form>
</template>

import { LightningElement } from 'lwc';


export default class CreateContact extends LightningElement {
    handleSuccess(event) {
        console.log('onsuccess event recordEditForm',event.detail.id)
    }
    handleSubmit(event) {
        console.log('onsubmit event recordEditForm'+ event.detail.fields);
    }
}


<?xml version="1.0" encoding="UTF-8"?>
<LightningComponentBundle xmlns="urn:metadata.tooling.soap.sforce.com" fqn="createContact">
    <apiVersion>48.0</apiVersion>
    <isExposed>true</isExposed>
    <targets> 
        <target>lightning__AppPage</target>
        <target>lightning__RecordPage</target>
        <target>lightning__HomePage</target>
        <target>lightningCommunity__Page</target>
    </targets>
</LightningComponentBundle>