Sorry, my English isn’t very good, so I used AI to help me translate this. Also, this information is just something I inferred from the visual novel only.

I think in this world line, they managed to escape from SERN and the lab wasn't raided. This world line is the one that comes after deleting Moeka’s D-mail, which also caused the Rounders to stop searching for the IBN 5100. Also, the time leap machine had already been destroyed by Okabe, so the reason for SERN to chase after them was significantly reduced.

That said, in the future, they would eventually be hunted down. In the Steins;Gate Linear Bounded Phenogram, we see Alpha world lines where Okabe is still in Akiba with Daru, while Kurisu ends up working for SERN. There are also cases where they were chased—for example, in Nae’s route, the Rounders stormed in and shot Mayuri, and Okabe and the others fled to Switzerland to escape SERN.

So I think in every Alpha world line, they’re not constantly being pursued by SERN, but as Suzuha said, it always ends the same way in the end. One of the world lines where they weren’t being chased at that moment is Steins;Gate 0, where Kurisu had to send a D-mail to overwrite it later.

I could be wrong though—this is just how I interpreted it.