The world of Weathering is a Next Sunday A.D. setting not noticeably different from reality when it was first released. What causes it to change so drastically in the intervening 25 years that humanity has developed Faster-Than-Light Travel, single stage to orbit Humongous Mecha and the warships needed to act as their carriers? Evidently, the flooding of Tokyo was the kick in the pants needed for the world's space agencies to get serious about having an offworld escape plan.
As to why Mikako and Noboru never mention it? Well, they are Saitama residents and Tokyo never comes up in their talk. Assuming the flooding was confined to Tokyo and never spread to the rest of the Kanto region, then around 20 years later it would just be a fact of life they hadn't even been around for. To contextualize for American readers, this is like a pair of average New Jersey teens as of this writing in 2020 not seeing a need to bring up 9/11 all the time.
Some fans have theorized that Hodaka may be one. If that’s the case, his and Hina’s relationship may be a difficult one.
The film takes place in summer of 2021, while Taki and Mitsuha's reunion takes place, most likely, in spring 2022, but definitely after October 2021 given Taki's meeting with Miki on the anniversary of the disaster. However, in Weathering with You's timeline, Tokyo is supposed to be under the eternal rainfall by then, meaning their reunion couldn't possibly take place in the very much sunny morning where Your Name wraps up. This opens up some other questions, like if they indeed get to reunite, or even if the events of the movie took place at all in the new continuity, such that Mitsuha's presence in Tokyo in WWY is not due to the destruction of Itomori.