Yes, just as the article said, and just as I have acknowledged in other posts in this thread.
You seem to have misunderstood what I meant by "third generation SE". The device coming next year is an update to the second generation SE. The third generation SE refers to the 6.1" replacement rumored to be coming in 2023.
If a change to in-screen Touch ID is not viable, then they will simply retain Face ID.
That doesn't stand up against your claim that "Apple wants to keep it cheap". A device based on the iPhone 12 Mini would not be cheaper any than one based on the iPhone XR/11. In fact, given the OLED screen it would likely be more expensive.
Furthermore there is no evidence Apple intends to discontinue the SE. In fact, multiple rumors suggest exactly the opposite - that it will see a third generation. This only makes sense since it allows Apple to continue to offer a low cost device that will be supported longer than the device on which it is based by combining the older technology with a new processor.