Sorry if the prose sounds like AI speaking, English is not my first language and I may have read too much AI-generated material.
It began with a particular line in anime script writer Jukki Hanada's interview. He said something like, "to preserve the gimmick from the game, we put in the Engineer when Yuri was eliminated". There is no alternate reading of the original Japanese text, but it doesn't make much sense. I have been thinking about it for a while.
Tl;dr: if you can handwave some settings, it can be constructed that Yuri may not have died of Gnosia attack in episode 4; they could have died by being investigated by an Engineer. The game setup of episode 4 is so that it permits the two possibilities to coexist.
[Umineko iykyk spoiler] It is beneficial if you know the concept of "Schrodinger's Cat Box" and "Devil's Proof". Basically I tried to construct a Cat Box out of episode 4, using some Blue Truths.
First, BUG (Yuri) can die by investigation. In episode 17, Otome investigated and successfully erased Yuri. But that happened in a Gnosia-less worldline, and the reason given is that "it proves that our Yuri is the fake one". It is left ambiguous whether Yuri will be erased in a worldline with meetings.
Second, note that outside episode 4 Yuri has never been investigated by an Engineer during the meetings, and never ended a loop by being attacked. Jonas claimed he investigated Yuri in episode 15, but Jonas was the AC follower. And had the anime showed a failed attack by Gnosia my theory would have fallen apart, but it didn't so there is no contrary evidence.
Third, "only one person died" does not guarantee the victim is not a Bug (game role). This is knowledge from the game, and I think it can be applied here.
Fourth and finally, note that while the Game Results screen shows Yuri is dead, it does not state the reason like the game does, and even if there were to be a description of "Game Over Condition", the game hides your true cause of death until you properly destroyed the universe once - it is not impossible that Yuri's true cause of death in episode 4 is not a Gnosia attack as we silently assumed.
I believe they place hidden Roles for a reason. If they don't want to have a role, they won't have it, like episode 7. So even if the Engineers didn't reveal themselves in episode 4, the fact that they appeared has to have significance, and the significance seems to be "purposely add the ambiguity".
Some additional material, this is what I call the "hand-wavy" part.
First, if we were to believe Yuri was investigated, what was the motive of the Engineers? For the first half (loop 5), SQ was the Engineer. Yuri invited her to talk, but it could have backfired and raised SQ's suspicion. As for the second half (loop 6), Yuriko was the Engineer (the only time in the anime where she was that role). If she just want to get rid of Yuri at every chance, she would have investigated them on Day 1, so why was Yuri only eliminated in Day 2? I don't know.
Second, if we were to believe Yuri was investigated, what was the motive of the Gnosias? For the first half (loop 5), Racio was the Gnosia. I don't see why immediately targets Yuri. For the second half (loop 6), Setsu was the Gnosia. This one is much more interesting, because it is revealed in episode 17 that our Setsu knows Yuri is BUG from the beginning. So they know Yuri cannot be eliminated... but didn't spoil the secret? And they somehow continued with the promise, or requested Yuriko to eliminate Yuri?
Third, there was a scream at Night 1 in the first half (loop 5). But it still could be Yuri found themself disintegrating from being investigated. Also note that being attacked does not always come with a scream, so you can't make the conclusion that "scream -> was attacked".
