my app relies on having an internet connection while it is running
In that case, you have the choice of either checking the receipt on the device or on the server. I guess there are pros and cons to each. Do you have code running on the server to support the app, or does the app just download files? If you have code running on the server you may prefer to extend that to do the checking.
What is your threat model? Are you aware of people actually cracking your app?
Should I continue using the verifyReceipt endpoint from the device?
What you're currently doing will continue to work, but it is not ideal as described above.
Should I plan to use the verifyReceipt endpoint from my server?
I wouldn't recommend that for new code as it's deprecated.
Should I plan to use the App Store Server API and App Store Server Notifications V2?
You could do that (though I don't personally know much about that).
Your other option is the validate the receipt on the server without communication with Apple.
There is a page titled "Choosing a receipt validation technique" here:
https://developer.apple.com/documentation/storekit/in-app_purchase/original_api_for_in-app_purchase/choosing_a_receipt_validation_technique