I feel like Restructured already requires us to live with this plot hole since the Senate (the entire Republic as it’s portrayed in the film?) is the obvious target.
My headcanon for rationalizing the lack of evacuation:
-Leia could simply be stating their best guess as to the target, but they don’t know for certain of the target or if the weapon will even work based on its new technology.
-From a logistical perspective it would probably take days or weeks to evacuate everyone from the entire Hosnian system (In reality it would probably take months or years, but I’m being generous).
-It seems that the Resistance has protocols in place that prevent it from simply transmitting electronic communications directly to the Republic to retain anonymity, which is why they sent one of their officers in person, presumably with some course changes along the way. It might take more time to safely alert the Senate of the danger than it would for the weapon to fire, so the Resistance would have negated that option out of hand.
-The film portrays the Republic as run by a bunch of Neville Chamberlains who clearly want to appease the First Order while secretly supporting the Resistance to fix the problem. At this point in the story the Republic should have no knowledge of the status of the weapon unless they are getting intel from the Resistance, so starting an evacuation would be a de-facto declaration of war with the First Order which many in the Senate are desperately and perhaps even illogically trying to avoid.
Leia might even suspect that the First Order is pointing its weapon at the Republic merely to test the anonymity of the Resistance (Remember, they know that Finn has defected to the Resistance with knowledge of the weapon), and Leia is hoping that retaining radio silence with the Republic will be enough on its own to make the First Order accept that the Resistance is truly working alone. This isn’t the fist planet she’s seen destroyed, after all, and in that case Alderaan was destroyed merely because the Empire suspected it to be in league with her. She’s probably desperate to avoid the same mistake, and recognizes that allowing the senators to escape in time isn’t worth the risk of the billions which will be left behind.
…
Whew, that turned into a bit of a novel. I wish there was more in the film about this, but I think these are reasonable extrapolations from the scant details we do get. My change even hints at this, since after Leia names the Senate as the target Poe clarifies that it’s the entire Hosnian system which is under threat.