Short answer: yes, rename it. Go ahead.
The FS25_ prefix is a GIANTS ModHub submission rule, not something the game engine requires. The game only cares that the name is letters, digits and underscores, and doesn't start with a digit. Renaming the zip to AAA_LogErrorExtractor.zip works fine.
So go ahead and Right click the mod, choose rename and then delete the FS25_ prefix.
- Your hotkey binding will probably reset to the default, since bindings are stored against the mod name. Just set it again in Options > Controls.
On why it's happening: your read is right, but the prefix isn't doing anything special. Mods load in plain alphabetical order. Aerator starts with A, the extractor starts with F, so Aerator loads first. Nothing is prioritising your mods — F is just late in the alphabet.
Worth being clear on what this does and doesn't change. The extractor's hooks are global once they're installed, so every mod's messages get caught after that point no matter what it's called. The only thing load order affects is messages a mod prints *while it is loading* — those happen before the hooks exist, so they're lost. Renaming to AAA_ moves that boundary as early as it can go and recovers them.
It still won't be perfect. Anything sorting before AAA_ loses its load lines, and there's a separate blind spot I can't fix at all: texture, i3d and shader messages are written by the engine's C++ side straight to log.txt and never pass through Lua, so the extractor can't see them regardless of when it loads. A clean report means clean as far as Lua reported it, not that log.txt is empty.
Thanks for flagging it — I'm looking at making AAA_ the default name in the next build.