Past or Plot?
Characters have lives outside the story. They are rich with anecdotes and memories. They all had childhoods, and bad jobs, and love affairs.
Good writing is often about showing the richness of a character's life through small 'tells' (borrowing the gambling use of the word 'tell' as an unintentional reveal). Perhaps the plot pushes them in a certain direction and they don't react as expected. That difference will jump out and call attention.
There's a very minor character in The Maltese Falcon, a woman who works in a book store. The MC tries to bluff her and she suddenly drops her pleasant store clerk attitude and pushes back. She has no actual backstory but instantly becomes a character with her own agency and opinions. She may work in a bookstore but she is not naive about creepy men who are lying to her face, years of experience implied through a simple exchange that did not go how the MC expected.
Character-building
When a character's personal history informs their decisions and behavior, it's characterization. We see their emotions, we hear their words, but if we're not in their head (like Jane Austen's free indirect speech) we will infer a backstory – and a current story – to make the 'tells' make sense.
The exceptions to 'tells' are characters who are closed books who reveal nothing about themselves, and characters who are so naive they were literally born within the story or for whom 'becoming aware' is the plot. The first stoic-type never reveals their history (at best the reader sees cracks through a wall, implying 'depth'), the latter type is slower than the reader, typical in coming-of-age and genres where the MC must discover a truth (mystery, horror, wonder, self-discovery). These characters' 'tells' may be when they don't react, or when their reaction is completely divorced from what is happening on the surface (implying unresovled internal conflict). It's still a personality 'tell' but it is a misdirection or defense to hide their real feelings: depth without specifics.
It's always a good idea to force the reader to supply some answers, especially when characters have complex (seemingly contradictory) reactions. If the reader is actively connecting the dots, they are engaged with the story and characters. What the reader imagines is usually stronger than what the author can write.
Does it belong in THIS story?
Historical elements that are about the current conflict – that is, specific events that happened earlier (before the opening of the book) that are are crucial to understanding THIS plot, belong in THIS story.
Obviously, they don't need to be spelled out in a prolog, they can be discovered, or teased, or even withheld from the MC's POV – all depending on the MC's path through the events. As author, you must make dramaturge decisions what to show the reader and when. Let's face it, readers have other entertainment so don't waste their time by wandering off on a tangent. If you are lucky enough to get a reader engaged in THIS story, do not derail with an unrelated side-quest in the middle of it.
An MC-as-narrator, or a 1st-person limited POV narrator, is usually misreading something about the current situation – if not straight-up 'unreliable' by lying or misdirecting. MCs need to be naive, not omniscient, or there is usually no story. The MCs journey is the reader's journey – for that reason the protagonist needs to stay focused on the present conflict, and telegraphing the current barometer of what the reader should feel (in the moment, more than a catalog of factoids and anecdotes).
So that is where you'll need to draw the line. Your MC is richer than the current story, and you do need to show that constantly. Characters that are not richer than the current story are not even characters, they are just props.
However, any backstory that takes up pages must be earned with a set-up and pay-off in THIS story. Readers are extremely savvy with filling-in-the-blanks. That's why genres use tropes to get to the action faster, and then must subvert those tired tropes later on – it's not enough to just introduce a trope and leave it there. Calculating how much side-plot fits in THIS story involves calculating additional characters and locations that will need pages to develop, and pay-off.
If the backstory is too interesting…, maybe check that you aren't over-writing it. If it has it's own conflict arc it might be a stand-alone prequel, but if it's stealing thunder from your intended plot that could be a finish-what-you-started problem.
On the other hand, the prequel might be the better story.
