if you wanted to change subscription price after 1st payment, set logic in your webhook controller,
in webhook use subscriptionId to find the subscribedObj, and take out the item that needs to update and call stripe update api,

    const session = event.data.object 

  const subscriptionId = session.subscription as string;
        const subscription = await this._stripeInstance.subscriptions.retrieve(subscriptionId, { expand: ['items'] });
        const item = subscription.items.data[0];
        await this._stripeInstance.subscriptionItems.update(item.id, {
          quantity: 1, //in my case i need to update quantity you can update price
          proration_behavior: 'none',
        });