Confirmed. I've got two PS4's and two separate Keyboards both wireless. (my wife plays with me a lot)

Both keyboards have the exact same problem as the OP and numerous other players. It's been confirmed on Reddit a few weeks back as well. I've also had trouble with the controllers sending repeating signals such as the rrrrrrepeating keys that others have mentioned. I have no way to confirm it, but I think the PS4's bluetooth hardware is a bit wonky.