This reminds me of something that Arnold Schwarzenegger wrote in his autobiography. He said that he was sent a lot fewer and different scripts after his double heart bypass surgery in the late 90s because studios were worried about insuring him and about audiences not accepting him as an action star any more. I wonder if Chadwick might've been worried that making the news public would similarly harm his career just as it was really taking off. He did play a superhero, after all. It's quite possible that what Arnie experienced was just how it was in the 90s and that it probably wouldn't happen today, but you never know and you can't blame Chadwick if he didn't want to take any chances.
Alternately, or maybe in addition, he may've kept the news to himself so that he could escape from it. By not making it public, he was able to go out in public and work without people bringing it up or treating him differently when the last thing that he wanted was to be reminded of it. It seems like he might've been an intensely private person, which I can relate to.
One last thought: it seems to me that the pandemic likely played a role in this coming out of the blue like this. Without it, the projects that he was slated to be in probably would've advanced and he would've had to have told people that he was too sick to film or attend meetings, which might've led to rumors. Instead, he just happened to have his condition deteriorate while everything was paused and everyone in Hollywood was stuck at home, anyways.