Korg keyboards such as the Pa3X and Pa1000 have songbook functionality. This lets you specify information such as tempo, time, instrument, voicing, and effects to be preconfigured for that song. You can use the MIDI capability within OnSong to change songs on the keyboard using Non-Registered Parameter Numbers.
Once you've connected your iOS/iPadOS device to your keyboard via MIDI, you can change your songs to send MIDI. To do this with a text-based chord chart, tap and hold on to the song title in the Song Viewer to open the Section Mapping Menu. Choose the MIDI tab and tap on the + button to open the MIDI Editor. This will let you add MIDI to the list of MIDI events to be sent when the song is loaded.
Once the editor is open, choose the NRPN option in the list and then choose the channel of the device or all channels. Next, set the Coarse Parameter to 2 and the Fine Parameter to 64. This is how the Korg keyboard will know you are wanting to communicate a song change. Next, determine the song entry that you want to choose. The Korg songbook shows numbered entries up to 9,999 options. You'll want to set the Coarse Value to handle the thousands and hundreds of that number (the left two digits) and use the Fine Value to handle the tens and ones (the right two digits). For instance, if you want to choose song entry 77, you would set the Coarse Value to 0 and the Fine Value to 77. If you wanted to choose song number 1240, you would set the Coarse Value as 12 and the Fine Value as 40.
When you're all done, tap the Done button to save your MIDI event to the list and then again to save the MIDI event list to the song change. Now when you load that song for the first time or tap on the title of the song, the MIDI will be sent and load the proper song entry on the Korg keyboard.
If you are not using text-based chord charts, you can still send MIDI but must do it through the Song Editor. To do this, view the song and then tap on the "A"/cursor icon in the Menubar to open the Song Editor screen. Locate the "information" icon in the Song Editor Menubar to open the Metadata Editor Menu. Scroll to the bottom and choose MIDI Send option. You can then repeat the same steps as above to specify MIDI events to be sent when the song is loaded. When you are finished, tap Done to set the metadata of the song and to save your changes.