Kinoku Nasu truly hit the jackpot with Fate/Stay Night in 2004, as the broad formula of its story has been remixed into countless side stories, to say nothing of stories that don't even involve a grail war. But with all these stories seemingly stemming from the original VN, it begs to question if one of the three routes in Fate/Stay Night is considered canon.
There's been Fate in Imperial Japan (Redline), Fate but with double the number of characters (Apocrypha), Fate in a virtual world (Extra), and Fate in America (Strange Fake). However, even when notable characters from Fate/Stay Night show up as Servants or cameos, rarely does the story tend to acknowledge the origin of the franchise.
The Fate Multiverse
Works written by Kinoku Nasu or even based on the world created by him tend to be called the Nasuverse by the fans, but this doesn't imply that each story shares continuity with another. The worlds share settings, iconography, and mechanics such as magecraft, but quite often, these stories are completely standalone.
It's like Elseworlds stories in comic books; you don't need to fret about where it fits in a timeline, just focus on a singular story and what it has to say. Some stories are so disconnected that drawing even the slightest link between it and F/SN seems foolhardy, while others are very explicitly set in alternate timelines.
Fate/Apocrypha exists in an alternate timeline that suggests that there was an alternate outcome to the third Holy Grail War, which resulted in an even larger war in the 2000s. This is very similar to the plot of Fate/Strange Fake, which also diverges after the third Grail War and results in a large and messy conflict in the American west.
For as many Fate projects that have come out since 2004, very few of them directly follow the events of Fate/Stay Night so far as to claim a canon route of the three. F/SN's story was just one significant but ultimately isolated incident in a large world full of crazy events, so while the event itself may be referenced, the outcome is rarely a matter of import to those that weren't there.
The Sequel
With all of that said, there is one visual novel that is a direct continuation of Fate/Stay Night's story, but it's not exactly cut and dry, if it was, this would have been a much shorter article. Released in 2005, Fate/Hollow Ataraxia is a sequel to the original VN, a story that anime-only Fate fans might not have heard about if they haven't explored Type-Moon's wiki.
Hollow Ataraxia begins 8 months after the events of F/SN, but after an experiment of Rin Tohsaka's goes awry, Shirou Emiya finds himself in a four-day time-loop. The loop begins on the fourth day of the Grail War from F/SN and continues until Shirou and a new protagonist, Bazett Fraga McRemitz find a way to break it.
Perhaps it seems like the article is burying the lede but unfortunately, this sequel is no less murky about the true canon ending of Stay Night. If anything, Hollow Ataraxia is a sequel to the entirety of its predecessor, or put another way, isn't actually a sequel to any of them. It functions almost as a counterpoint to Stay Night. It's a dream world colliding all three routes into one, and though there is a world outside the dream world, the canon route is still never specified.
To aspiring Fate fans who might be rummaging through articles about the lore, anxious to understand so that they can jump in, the above explanation might be quite vexing. However, just as there are things that demand explanation within storytelling, there are also things that are never meant to be explained, and Fate/Stay Night truly doesn't need a canon ending.
Don't Overthink It
After all, it makes quite a bit of sense that this franchise full of disconnected standalone stories stems from a VN that itself had three distinct paths/possibilities experienced one after the other. And through this very game-like conceit, Nasu was able to explore the theme of the self and ideals in three dramatically distinct ways that resonate with audiences differently.
Creating a canon route almost feels wrong, because it's like opening the box to look at Schrödinger's Cat; suddenly the possibilities and multidimensionality converge. Now instead of fans being able to pick their favorite, there's an invisible line that says that only one of the stories is "real" and that would invalidate so much of Fate lore as to render the media's strides inert.
In Fate/Complete Material III, an encyclopedia on the Fate universe, Nasu was asked: "Is it safe to assume that Hollow's "Sequel" follows none of the three routes’ endings in Fate/Stay Night?" Nasu responded thusly:
"It's best if you don't think too much about it (laugh)."
- Kinoko Nasu, Fate/Complete Material III, p.136 (Released October 29, 2010)
When people consider "universes" in media, they tend to think of very rigid, tightly constructed continuities with an overarching plot and a dedicated adherence to canon. However, sometimes it's important to remember that a singular piece of art should also be able to stand alone. The Fate universe is hardly just one universe, and more a clash of competing possibilities.
But so long as each individual piece of art that catches the eye has something beautiful to offer, or cool to show, or poignant to say, then maybe what's "canon" doesn't quite matter. The kind of hero that Shirou Emiya became by the end of each Route will speak to every fan differently, and in that, all three may as well be canon.
Source: Type-Moon Fandom Wiki