If someone asks, "What day is it today?" and it is 10 pm, is it correct to respond with
"Today was Tuesday."
since the day is over and it's night? Is that response incorrect? Should the correct response be
"Today is Tuesday."?
You could only say "Today was Tuesday" if it's midnight and Tuesday has passed into Wednesday.
"Day" can mean both "period of light" and "24-hour calendar slot". Which one depends on context. By asking "what day is today?", the implied context is more likely to be the second one, since 'what day' expects a calendar answer.
If someone instead said "Isn't it a lovely day?" as the sun is setting, then you could respond "It was a lovely day" since the implied context is more likely to be the period of light.
Today has been a bitch! It's only 11 a.m. and things aren't going all that well. Restaurant employee problems. But it's still Wednesday here in Taiwan.
At 10 p.m., if I decide to go to sleep and not get up until tomorrow, then I'll say "Today was a bitch!" because the day will be over for me, even if you stay up till midnight. But it'll still be Wednesday here in Taiwan. So if you were to ask me "What day is it today?" before I nodded off, I'd say "It is still Wednesday, as far as I know".
Tense is relative to events, not necessarily to the clock. And some theoretical physicists tell us that time isn't real anyway. Others say that it bends along with space, which still others allege is vacant. No wonder tense and the sequence of tenses are so confusing. Especially for everyone who lives in countless alternative universes.
I live in my own universe, a universe for one: Corvette.