Yet, in America, people say things like "do you have plans for the weekend?" Or, "What did you do last weekend?"
Nobody ever says, "Do you have plans for the upcoming two days which, respectively, constitute the end of this week and the start of the next one?"
So, Americans and Brits are inconsistent. They have "the weekend" which is a block of two days when salaried people with regular working hours don't work; and they have Sunday as not the week end, but rather the beginning; or the "front end" of the next week. Which means that the two days cannot be the weekend; they are two different ends of two different weeks.
> that's changing (by convention)
It's changing because people have to confront the above reasoning and realize that a week beginning in the middle of something that they have been calling "the weekend" for decades is silly.
I believe in my entire life I've encountered exactly one situation in which the day that is defined as the first day of the week actually made a difference to anything: my kids' swim school schedule, where Week N of the term runs from Sunday through to the following Saturday inclusive.
Since the working week (and the school week) here starts on Monday regardless of whether Sunday or Monday is regarded as the first day of the week, it seems to have always been a distinction without a difference to me.