I want to build an iOS VPN app for personal use only, so I need to add the NetworkExtensions capability (according to my understanding).
From Apple's documentation on "Adding Capabilities to Your App": The platform, and whether you're a member of the Apple Developer Program, may limit the capabilities available to your app. The documentation doesn't explicitly say which capabilities require being a part of the Apple Developer Program. I also don't see why I'd need to be a part of the Apple Developer Program to write software for personal use. Note that, at least to my knowledge, the NetworkExtensions capability does not depend on any service from Apple (as opposed to HealthKit or Game Center).
So is there a way to add a Network Extensions capability to an iOS app without joining the Apple Developer Program?
The capabilities associated with each program level are shown in this table
The first column in the table is the (paid) Apple Developer Program. The middle column is the Apple Enterprise Developer Program. The last column is the (free) Apple Developer level:
The free tier "Apple Developer" cannot add network extensions or personal VPN capabilities.
You will need a paid Apple Developer Program membership.