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I would say British English seems to adhere to English grammar books that I learned in school more than American English.
For example, I was taught that we use present perfect with "ever" because the time is unspecified or something which happened in the past which is important now.
See the Cambridge Grammar say:
Present perfect simple: uses
We use the present perfect simple to refer to events in the past but which connect to the present.
We often use present perfect for talking about something which happened in the past which is important now.
we often use general time expressions like ever, never, before, in my life, so far, up until now with this use of the present perfect simple:
We often use ever, not … ever and never when we talk about experiences:
Have you ever tried to write your name and address with your left hand?
In American English the past simple is often used instead of the present perfect simple, often with already and yet.
American English Did you eat (yet)? Did you finish (already)?
British English Have you eaten (yet)? Have you finished (already)?
Another source confirms this:
The Present Perfect Tense in British and American English
British and American grammar differences – present perfect vs. simple past
In American and British English, we can also use ‘just’ with the simple past to talk about recent events. So what’s the difference about the way American and British people use ‘just’? When we’re giving news in British English we generally use the present perfect.
Oh, your mother’s just called.
Oh, what did she want?
When we’re giving news in American English, we often use the simple past.
Your sister just called.
Oh really? What did she want?
So both these sentences are possible in both varieties. It’s just that we use the present perfect more frequently in British English.
The words ‘yet’ and ‘already’ indicate a time up to now or until now.
That relation to the present time means we commonly use them with the present perfect. That’s true in both British and American English. In American English, especially spoken English, you’ll often hear us use these words with the simple past, too.
I’m going outside to practice soccer.
Wait a sec.
Did you do your homework yet?
Yeah, I already did it.
In British English, these sentences would be unusual. With ‘yet’ and ‘already’ we usually use the present perfect, not the simple past. So when do Americans use the present perfect and when do they use the simple past? In written English and when we’re speaking carefully, we often use the present perfect with ‘yet’ and ‘already’. But when we’re speaking informally, we often use the simple past. ‘Did you do it yet?’ sounds a little more informal than ‘Have you done it yet?’, especially if we use the less careful pronunciation ‘Did ja do it yet?. And there’s something else. My theory is ‘Did you do it yet?’ can sound just a little more urgent in American English than ‘Have you done it yet?’
And I guess that usage may apply to "ever" as well
Have you ever watched the film? ( we use present perfect because we don't know the time the that person watched the film or the specific time that that action happened is not important or its result is important now, ie I just want to know if you have watched it, the time is not important)
But American people will say:
Did you ever watch the film? (I feel strange when hearing it, why would the asker want to know the specific time right at the beginning)
Is that how American people say daily? or American grammar is not as strict as British English?