Back in 2017, Sony was planning to launch the PlayStation Now cloud gaming service on mobile phones, according to a leaked document sourced from the Epic v. Apple trial by The Verge.
An Apple document referenced an unannounced "mobile extension of an existing streaming service for PlayStation users, streaming access to over 450+ PS3 games to start, with PS4 games to follow."
No such mobile device expansion ever materialized. PS Now is still available, offering PS4, PS3, and PS2 games that can be played on PS5, PS4, or Windows PCs, but there has never been a version for iOS or Android, nor has PlayStation made it available for the Mac.
Apple may have been discussing PS Now because at the time, it had started work on the Apple Arcade gaming service that ultimately launched in 2019.
Sony was early to cloud gaming with PS Now. It launched in 2014, years before its competitors were working on cloud gaming offerings. GEForce NOW followed in 2015 in a beta capacity, but Google Stadia didn't launch until 2019 and Xbox Cloud Gaming didn't come out until 2020.
It's not clear why Sony never followed through with a mobile version of PS Now, as the software would have launched before Apple introduced strict cloud gaming rules in the App Store with the debut of Google Stadia and Xbox Cloud Gaming. The Verge speculates that Sony decided it wasn't worth taking on Apple at the time, or that Sony may have decided to focus on console sales instead.
Sony does have Remote Play for accessing Sony games on various devices, but Remote Play requires a PlayStation console, while PS Now does not. Rumors suggest that Sony could in the future unveil an updated cloud gaming service to rival Xbox Game Pass, but it is unclear if the new service will come to mobile devices. If so, Sony will likely need to take the path that Microsoft and Google took, offering a web-based solution on iPhones and iPads.