I followed this guide to the letter (except for not needing to install libfaudio0 on Linux Mint 20) after being encouraged by these comments on the PSO subreddit promoting the reopening of this server.
I had precisely the same error as encountered above after installing the game through PlayOnLinux (4.3.4), with Wine 5.0.2 (I also tried using version 4.7), mono 188.8.131.52, and gecko 2.47.1:
online.exe crashed immediately, it wouldn't load at all.
Since the aforementioned guide was of use to others in the past, I had hoped it would work for me as well.
Edit: GameGuard isn't the problem, see SourSkittles' post below, their help was invaluable in making the game playable for me.