Since episode 23β is a prequel, Suzuha knows nothing of the plan. So either she simply doesn't know to bring it up, or she doesn't even know that Nakabachi's paper is the cause of World War 3.
Suzuha's quest to go back in time and make Okabe save Kurisu is almost identical to Okabe's trip to save Kurisu.
The events likely plays out as follows. Disclaimer, some of this is speculation:
In an attempt to stop World War 3, Suzuha goes back in time to make Okabe save Kurisu. This is episode 23β. The attempt fails and the events of Steins;Gate 0 begin.
Over the next 15 years, Okabe learns the situation and develops the plan to save Kurisu and save World War 3.
The plan has (at least) two parts:
1. Okabe sends the video D-mail to himself from 2025 to 2010.
2. Okabe communicates with Suzuha so that she will tell the 2010 Okabe about Nakabachi's paper, and view the video D-mail.
However, there is one important thing: The past must not be changed.
Okabe is told to trick himself into thinking Kurisu is dead so that it doesn't change the events in the original Steins;Gate prior to episode 23.
Likewise, when Suzuha travels to 2010 after the events of Steins;Gate 0, she must not change the past where Okabe fails once. So in episode 23, she behaves identically to herself in 23β so that Okabe fails once - thus ensuring that the events in Steins;Gate 0 do not change. This is part of the plan.
Only afterwards does she make her move which triggers Okabe to try again and enter the Steins;Gate world line.