Retrieving custom metadata values in LWC

I have Custom Metadata Type values that I want to display in a Lighning Web Component. I've read a few different posts (post 1, post 2) about this but neither seems to work for my scenario.

My Custom Metadata Type (API name: Billing_Custom_MetaData__mdt) has a field (customerUrl) that I need to display in my component:

myLwcComponent.html

<template>
  <div class="slds-m-around_medium>
    <p>Web address: {customerUrlValue}</p>
  </div>
</template>

myLwcComponent.js

import { LightningElement, api, wire } from 'lwc';
import { getRecord } from 'lightning/uiRecordApi';
const FIELDS = [
  'Billing_Custom_MetaData__mdt.customerUrl__c',
];

export default class LifeCycle extends LightningElement {
  @api recordId;
  @wire(getRecord, { recordId: '$recordId', fields: FIELDS })
  metaDataRecord;

  get customerUrlValue() {
    return this.metaDataRecord.data.fields.customerUrl.value;
  }
}

I'm new to LWC so I'm trying to follow those posts and Salesforce documentation (Get Record Data) for correct information. However, the customerUrl value from Billing_Custom_MetaData__mdt isn't rendering in my component.