I've looked into this a bit, and yes, it is a bit older libfreetype fails to load game provided font, that is fixed in freetype version 2.11.1 (.so version 6.18.1) by commit 5b626281f1e6524dd87e3d5d6af795b39a8cc10b. I think this issue will likely wait until Steam runtime is updated to the fixed libfreetype version.
Compatibility Report
System Information
I confirm:
Symptoms
The game's main text disappears the second time the game is launched
Reproduction
The same bug also reproduces in Config / Text, the box below Text Display Speed.
To return to the functional first-run state, go to .../steam/steamapps/compatdata/377710/pfx/drive_c/users/steamuser/AppData/Roaming/Frontwing/Idol Magical Girl Chiru Chiru Michiru (Part 1)/setup.xml and delete either the <faceruby> and <face> lines, or just the entire file.
~The issue is caused by Proton's FreeType being too old. The issue reproduces in various Wine versions with LD_LIBRARY_PATH=.../steam/ubuntu12_32/steam-runtime/usr/lib/i386-linux-gnu/, and does not reproduce with system FreeType, nor does it reproduce if I set LD_LIBRARY_PATH to the sniper or soldier runtimes.~
The issue seems to be FreeType rejecting the font for whatever reason. The symptoms are the same as if using an outdated FreeType, but I can't identify the exact conditions.
(The game is also quite vulnerable to softlocks in Proton 9.0-3, but I fixed those yesterday. https://gitlab.winehq.org/wine/wine/-/merge_requests/6873)
On the first run, the relevant part of WINEDEBUG=gdi,font,dc looks like
(no, I don't know why the game passes a mojibake font name. The text shows up, don't worry about it)
The second run instead looks like
and running it in a Wine with newer freetype returns