I have created a React application where users can subscribe to a subscription and can also cancel the subscription, but I am wondering what are the ways and how can I receive the transaction details that automatically occur every month?
You are looking for Webhooks
The event names for Subscriptions are listed here: https://developer.paypal.com/docs/api-basics/notifications/webhooks/event-names/#subscriptions
Another way, of course, is to log into www.paypal.com and go to Activity -> Reports and do an Activity Download, which can be in csv format