What tenses are being used in this sentence construction?

A new book* is being released with the tagline

If you knew how your love story ends, would you dare to begin?

I'm a native British English speaker, the author is, and I presume whoever wrote that is as well.

It isn't a construction I'm familiar with. I've tried substituting other verbs in, and haven't managed to get a sentence I would say yet. For example

If you knew you catch a cold tomorrow, would you go out?

If you knew a bus hits you in London, would you travel there?

I'd choose to say either

If you knew you were going to catch a cold tomorrow, would you go out?

or

If you knew you caught a cold tomorrow, would you go out?

I can't believe a publishing house would put that on the front cover if it's incorrect though. So what exactly is going on?

*For context, when the main character kisses somebody, she can see how they will die. She doesn't know whether it's the kiss that decides their fate, or she can just see what will happen to them. She stops kissing people. This is obviously a problem when she meets a man she falls in love with.

Short answer: I think "ended" would be better, because it appears within a conditional mood clause.

Long answer:

I don't think this is a Literary Present issue, or even really a tense issue. More at issue is the Conditional Mood.

In the Romance languages (probably Germanic languages too, but don't quote me on that), moods are a categorization scheme for verbs separate from the tenses. Rather than telling you about the time of interest, the mood tells you about the purpose of the sentence or clause: to make a factual statement, propose a hypothetical situation, make an order or request, or what have you. Any given verb might have a different form for each tense-mood combination.

English has only retained vestiges of these mood rules, and you've found one of them. The sentence you bring up is a counterfactual conditional (Second Conditional in that first wiki link): It describes something you know isn't the case (but just pretend for a minute). This is in contrast to situations where you don't know the reality (e.g. "If it rains tomorrow") or situations that are the reality sometimes ("When it rains"). Counterfactual conditionals use a past-tense construction, even though the sentence is talking about the present.

So, based on that, it's definitely correct to say "if you knew". The extra wrinkle comes because there's a subordinate clause "How your love story ends". Does a subordinate clause in a conditional-mood context inherit the conditional mood? I haven't seen a rule about it in print anywhere, but it seems to me like it should, since it's still part of the condition. On those grounds, I'd say "how your love story ended" would be better.

It’s fine; it’s the literary present (also called the historic present or narrative present):

In English grammar, the literary present involves the use of verbs in the present tense when discussing the language, characters, and events in a work of literature.
_{Source: ThoughtCo.—literary present (verbs)}

Like this:

How does the love story end?

Romeo returns to Verona because he believes Juliet is dead. When he arrives at her tomb she appears lifeless, and in his grief he kills himself by drinking poison. Moments later Juliet wakes, and, finding Romeo dead, she plunges his sword into her breast.
_{Source: Sparknotes—Romeo and Juliet}

A lot to unpack here! Let's start with the cheap shots:

I can't believe a publishing house would put that on the front cover if it's incorrect.

Oh... I would. I would indeed.

Okay, now that I've got that out of my system: I think the friction comes from the intersection of narrative and reality. Or, to put it less abstrusely: stories have their own "present." We're all familiar with literary present tense, in which we can say "Hamlet kills Polonius," without having to quibble with the fact that he first killed him around 1600. Gilgamesh and Ted Lasso share an abstracted present as we sit outside of their timelines.

It is this, really, that lets "how the story ends" become enshrined as a phrase of its own (just Google it and you find the titles and lyrics of at least a dozen songs). So to my view, "... how your love story ends" is simply literary present.

The friction you're feeling is because the hypothetical challenge positions you, the reader, as a character in the narrative. To the Hamlet of Act II, "what's past is prologue" (to mix references). The character within the narrative is conscious only of the linear flow of time. This sentence positions us dually as literary critic, knowing "the story," and as an agent within it, poised to enter the linear stream. This gives us a sort of Cubist view of both the timeless and the timed at once, thus your cognitive dissonance. "If you knew, Mr. Hamlet—wait, I mean know?—that it was—is—will be Polonius behind the curtain, would you/will you/won't you—oh dear..." A certain degree of verb-tense confusion is inherent in the premise of the challenge, knowing "how the story ends" when you have still not "begun"—we are to know the end from before the beginning?

So yes, in my view, the literary present saves us from a Star-Trek level of confusion about how the timeline interacts with itself. In fact, I could see using it even in a simpler conditional construction in which we aren't meta-actors:

If you knew how a book ends, would you choose to begin it?

Yes, this strains grammaticality, but I would defend it because Hamlet (spoilers) ends tragically, whether you conditionally "knew" it or not going in. So even though your knowledge is conditional, and you would normally pair it with a past tense, the literary present is unaffected by your condition.

Is the way it's written acceptable?

Well, obviously it was acceptable to the publishers, and it clearly got its point across. This treads into subjective territory, but to my mind, the "punchiness" of the streamlined version is not a mere gimmick, but improves the conveyance of the meaning.

If you knew how your love story ends, would you dare to begin?

If you knew how your love story were going to end, would you dare to begin it?

There's certainly a pleasing assonance in "ends ... begin," which is lost if we stick on an object, "it." And the published version even (surely accidentally) conforms to an anapest meter, while any past tense must disrupt the unconscious scansion.