It seems like you've already taken the appropriate steps by contacting both Netflix and Apple support. If picture-in-picture (PiP) works with other applications but not with Netflix, it's possible that this is a limitation imposed by the Netflix app itself rather than an issue with your device or iPadOS.
Unfortunately, if both Netflix and Apple support have been unable to provide a solution, there may not be much else you can do from a user standpoint. It's worth keeping an eye on future updates to the Netflix app or iPadOS, as these may address compatibility issues or introduce new features.
In the meantime, you may want to explore alternative methods for multitasking while watching Netflix, such as using split-screen multitasking or multitasking with other apps that support PiP functionality.
If the issue persists and becomes widespread among users, Netflix may eventually address it in a future app update. Until then, you may need to rely on other methods for multitasking while using the Netflix app on your iPad.