Those trademarks Siliconera discovered were indeed for a localized version of The Idolm@ster Shiny Festa rhythm games. While these aren’t idol training sims, Namco Bandai made English versions of the PSP games. However, these won’t be available for PSP, the localized The Idolm@ster Shiny Festa games are for iOS.
Recently, during a special year-end livestream, Bandai Namco Entertainment revealed that they are currently developing a new console game for The Idolmaster franchise. The game will be announced during a livestream that takes place on January 20, 2020 at 20:00 JST. It will be live-streamed on Youtube and Niconico.
Bandai Namco will end service for smartphone games The Idolmaster: Shiny Festa Harmonic Score, The Idolmaster: Shiny Festa Rhythmic Record, and The Idolmaster: Shiny Festa Melodic Disc on March 15, the publisher announced.
Michibiku's Jenni Lada writes, "Before deciding on a The Idolmaster game, we have to take a look at who you are and what you know. These are text heavy titles. How much Japanese do you know? There are entries that apply to people of all skill levels, so I’m sorting them by how much you do or don’t need to know."