Can an interrupted long rest be treated as a short rest?

[RSP]

You don't declare a long rest or a short rest. It's not a button you push marked "Long Rest" or "Short Rest".

You tell the DM you're resting, and how long you're going to try and rest. If you meet the criteria for a short rest, then you got the benefits of short rest. If you instead meet the criteria for a long rest, you get the benefit of a long rest.

The tweet is just saying that if you meet the requirements for both, you don't get both.

You absolutely can tell the DM "we take a long rest" or "we're going to take a short rest;" I've seen it in play plenty of times. Doing so would prevent later invoking the other, as again, they're mutually exclusive.

I'm not sure why you think it's not possible for players to declare what type of rest they're planning on taking.