Sadly, The Evil Within 3 has not (yet) been announced by series developer Tango Gameworks. However, if a newly discovered Easter egg tucked away in their latest release Hi-Fi Rush is any indication, an announcement may be coming soon.
Hi-Fi Rush is already rather full of references to The Evil Within, as GamesRadar+ has kindly pointed out. While all of those other references were fun little nods to the franchise, none have really seemed to hint at the possibility of a new game being announced. That is, none besides this newly discovered Easter egg.
Apparently, during the opening cinematic to Track 11: The Needle Drop, your group is taking an elevator ride to meet a character named Kale. As the elevator reaches its destination, there is a very, very brief look at a screen that shows you've arrived at floor 776. At the bottom of the screen is a news ticker that reads: "Sequel to popular survival horror franchise anounced [sic]."
That specific point can be seen at around the 7:40:50 mark in a full gameplay playthrough from YouTuber Shirrako. Just keep in mind that this Easter egg takes place near the end of the game, so don't watch for too much longer if you want to avoid spoilers.
Sadly, while it's possible that this is talking about a mythical announcement of The Evil Within 3, this is far from a confirmation of anything. It's at least nice to hold out some hope that this is a real indication of things to come, yeah? Besides the recently released Hi-Fi Rush, Tango Gameworks is also known for The Evil Within games and Ghostwire: Tokyo. I wouldn't exactly call Ghostwire: Tokyo a survival horror game, which narrows things down considerably.
