Per a recent comment from Respawn Entertainment's community coordinator, it seems the company is too busy to work on Titanfall 3.
According to community coordinator Jason Garza, there is nothing related to Titanfall currently in the works. He was asked for any comments on Titanfall, broadly, during a September 20 livestream. His response was pretty forward: “Don’t get your hopes up, man. I’ve said this before. We don’t have anything in the works. There’s nothing. There’s nothing there. We’ve got too many other games in the works right now.”
Indeed, it does seem that Respawn has a lot of games currently in development. Apex Legends, as always, is constantly getting support, while EA itself all but officially confirmed Star Wars Jedi: Fallen Order 2 during an earnings call. There’s even talk of a smaller team out of Respawn Entertainment working on a new IP, with no apparent room for Titanfall 3.