Let's consider a more charged situation; what if we were talking about crime and punishment:
You broke my cup. You must buy me a new one.
This is very direct speech, and might offend you. If there's any chance that I'm wrong, and you didn't break my cup, then I have wrongfully accused you. And I'm making an absolute demand that you buy me a new cup.
If you broke my cup, you should buy me a new one.
This is a bit more indirect. I'm not saying with certainty that you broke it, but I'm clearly saying that it's a real possibility. Either you did or you didn't.
If you were to have broken my cup, you would of course buy me a new one.
This is even more indirect, and the least likely to cause offense. I'm not even saying "if"; it's not as if I'm trying to decide whether you did or didn't. Instead, I'm talking about a hypothetical, talking the same way I would about something imaginary or in the future ("If I were to win the lottery..." "If you were to meet a dragon..."). It might be that I know, and you know, that the cup is very definitely broken, and by bringing up the topic it's clear that I'm thinking about you as a suspect. But by softening my language this way there's less chance for offense and a friendlier tone.
Many languages have similar "hypothetical" tenses, like Spanish Quisiera un vaso de agua.
Edit:
You asked about the difference only between two constructions, but you also mentioned a third:
- "If you provide, it will" —simple present plus future
- "If you provided, it would" —past plus hypothetical
- "If you were to provide, it would" —hypothetical plus hypothetical
You didn't ask about the difference between these second two, but: They can be seen as very similar, but note that the last one is a bit formal and the second is a slightly more casual and conversational version of the same thing. I might actually say "If you were to" in everyday conversation, but I'm a bit of an academic geek, and others might be less likely to use it in speech.
Edit: Is the speaker uncertain? The answer is Maybe, in some examples, but that's not the point.
This construction is all about getting someone else to do something. It softens requests, suggestions, or orders. In fact, your book goes a bit beyond giving a language lesson and is giving a lesson in behavior (or culture, anyway): When you're trying to influence someone else, it's more polite to allow some uncertainty into the situation than to make direct demands. Sometimes this can be a kind of euphemism: Maybe I know for sure you broke my cup; you know you did; I know you know, and you know I know. But I still use hypothetical language to avoid making you feel angry or afraid.
One of the examples from your book truly asks a question: "Would it be all right if I came around about seven tomorrow?" In this case of course the speaker is uncertain; they really want to know whether this time is OK. The more-direct, less-polite version of this might be "I'll come around seven tomorrow." This is less polite not just because of language, but because the speaker is making plans without consulting the other person, telling them how it's going to be instead of letting them have input.
In the example "If you were to provide context, it would help," the speaker doesn't know whether the hearer will accept this suggestion or not. But that's not the point. The speaker isn't asking a question ("Will you provide context?") or trying to resolve their own uncertainty. They're softening the direct command "Provide context!" by saying that maybe the hearer will do it, maybe they won't, but if they do, it will be beneficial.
Sometimes there is so little uncertainty that we use language that in some ways doesn't make sense when you look at it too closely. If a toddler wants a glass of water, they demand it directly: "Give me a glass of water!" Or they might state their definite desire: "I want a glass of water!" We teach them to soften these requests: "I would like a glass of water." We use "would," a word that we would usually use in a conditional ("would ... if"), but we don't even bother saying the rest of the conditional. Maybe it's something like "I would like a glass of water if you were to give me one." Maybe you will, maybe you won't; I'm not demanding or even saying that you definitely will, but if it were to happen... I would like it.