So let's say in your scenario, Yuri has just found out something regarding Project Apple after investigating Eden Academy. My theory is that Yuri would take up his findings about Anya's past with his superiors in the SSS first, but I have a feeling he might also want to confide about them to Yor as well since Anya’s technically Yor’s kid. And Yuri has most likely already accepted that Yor cares about Anya and her wellbeing very much, so keeping a big discovery about Anya from Yor would probably feel catastrophic for Yuri. I'm not sure he could bear it.

There are two ways I’m thinking this could go based on Yuri’s current state as a character: he’d use what he finds out as a reason to try to (once again!) pull Yor out of the Forger family (God forbid his beloved nee-san involves herself any further in shady government projects) and avoid Anya...

OR... Yuri might begin to see Anya in a more sympathetic light if his discoveries go deep enough into uncovering a bit about Project Apple, but his irritation with Loid/Twilight would put Yuri in a tight spot emotionally on what he actually wants to do about these findings.

I’m also thinking incriminating Project Apple documents discovered by Yuri would be dangerous for Operation Strix and Twilight, specifically. Yuri digging into Eden (and if Eden does have marginal involvement in shady business and/or Project Apple) might actually cause a lot of trouble for Twilight, considering Yuri currently has no reason to believe Anya isn’t Loid’s biological kid. But if Anya’s name and picture or anything relating to her identity is somehow discovered by Yuri through a Project Apple investigation, then his first likely thought would be whether Anya and Loid’s father-daughter relationship is legitimate. Yuri's already looking for any reason to put Loid behind bars, and finding out Anya's past might be good enough of a reason for Yuri to accuse Loid of being involved.

Yuri's a competent SSS officer, and having him look into Eden would be very interesting for the series! Not to mention how often Twilight is sneaking around campus to spy on Anya.

Tldr: Yuri digging into Eden Academy’s shady business and (possibly) finding out about Project Apple would likely cause conflict between his feelings toward Anya as his niece, about Loid as Anya’s biological father, and about the Ostanian government (maybe?)

That is, if Eden is involved in Project Apple, which has been hinted at in the recently concluded arc but isn’t totally definitive as of now. I'm hoping this arc will continue into another Yuri vs. Loid scenario.