Regarding the Matt Reeves Batman movie, the Washington Times article says Matt Reeves is starting fresh on the screenplay, which means The Batman movie release date is several years off. It's noted with the release date potentially being years away, that it leaves open open the possibility of further changes regarding the casting of Ben Affleck as Batman, something which Ben Affleck recently confronted as well; however, Charles Roven offers:
“From everything I know, he’s going to play that Batman. They’re retooling the script, so I can’t really say anything for certain.”
Now regarding Man of Steel 2, the article also says it isn't coming any time soon, with Charles Roven offering an update in that there is no script for Man of Steel 2 as of yet, but “various story ideas” are being kicked around.
Regarding the release date for The Batman, we can speculate if Matt Reeves starts the script at the start of 2018, that filming can begin possibly at the end of 2018 or start of 2019, which may mean The Batman might not be released until 2020.
Hopefully Justice League is a big success and WB green lights more DCEU movies, which would include Man of Steel 2.