Stripe Charge Failing

I am on lesson 4 of the Stripe tutorial (https://laracasts.com/series/how-to-accept-payments-with-stripe/episodes/4) and while almost everything has gone well I've run into a problem when trying to complete the charge. The issue appears to be this line:

$product = Product::findOrFail(request('product'));

As when I comment it out and hard code a price value in rather than try and pull it dynamically the operation completes as normal and I can see the charge in my Stripe account. Looking in the inspector in Google the error I am receiving is: No query results for model [App\Product]

I tried to print the request using the log but when I check it, it is empty as there is no value attached.

Here are the various pages:

bilable.blade.php (not an error, accidentally mispelled it)

@extends('layouts.app')

@section('content')
<h1>Buy My Book for $25.00</h1>

<checkout-form :products="{{ $products }}"></checkout-form>

@endsection

CheckForm.vue

<template>
    <form action="/purchases" method="POST">
        
        <input type="hidden" name="stripeToken" v-model="stripeToken">
        <input type="hidden" name="stripeEmail" v-model="stripeEmail">

        <select name="product" v-model="product">
            <option v-for="product in products" :value="product.id">
                {{ product.name }} &mdash; ${{ product.price /100 }}
            </option>
        </select>

        <button type="submit" @click.prevent="buy">Buy Book</button>

    </form>
</template>

<script>
    export default {
        props: ['products'],
        data() {
            return {
                stripeEmail: '',
                stripeToken: '',
                product: 1
            };
        },
        created(){
            this.stripe = StripeCheckout.configure({
                key: Laravel.stripeKey,
                image: "https://stripe.com/img/documentation/checkout/marketplace.png",
                locale: "auto",
                token: function(token){

                    axios.post('/purchases', {
                        stripeToken:  token.id,
                        stripeEmail: token.email
                      })
                      .then(function (response) {
                        alert('Complete! Thanks for your payment!');
                      })
                      .catch(function (error) {
                        console.log(error);
                      });

                }
            });
        },
        methods: {
            buy(){
                let product = this.findProductById(this.product);

                this.stripe.open({
                    name: product.name,
                    description: product.description,
                    zipCode: true,
                    amount: product.price
                });
            },

            findProductById(id){
                return this.products.find(product => product.id == id);
            }
        }
    }
</script>

Purchases Controller:

<?php

namespace App\Http\Controllers;

use Log;
use App\Product;
use Illuminate\Http\Request;
use Stripe\{Charge, Customer};

class PurchasesController extends Controller
{
    public function store()
    {

        Log::info("Product Info: " . request('product'));
        $product = Product::findOrFail(request('product'));

        $customer = Customer::create([
            'email' => request('stripeEmail'),
            'source' => request('stripeToken')
        ]);

        Charge::create([
            'customer' => $customer->id,
            'amount' => 8000,
            'currency' => 'aud'
        ]);

        return 'All done';
    }
}

Web Routes:

Route::get('/billing', function () {
    $products = App\Product::all();

    return view('organisation.bilable', compact('products')); // no error here, I accidentally misspelled "billable" but couldn't be bothered to fix it for what I am doing.
});
Route::post('/purchases', 'PurchasesController@store');

Thank you in advance.

Edit: The solution was to recast this in the FormCheckout.vue file to be a separate variable as seen in the answer below.