So, cleaned up all liquidcrystal libraries from my ~/Arduino/Libraries folder.
Re-installed the built-in Arduino LiquidCrystal library (version 1.0.7), just to make sure
Installed LiquidCrystal I2C by Frank de Brabander (version 1.1.2).
This failed to compile for any board: LCD.h not found.
Turns out that belongs to NewLiquidCrystal which served me quite well on the Pro Micro and NodeMCU. So installed that one again.
Now it compiles when I set my board to Pro Micro or Uno, but not when I set it to ATtiny841. The same error messages as posted above still appear.
Indeed it looks very much like two software I2C implementations clash - but I wonder where the second could possibly be? I do expect that an LCD library does not try to implement a software I2C, but instead will just try to use the standard Wire library, and let Wire figure out how the I2C works under the hood.
I also tried LiquidCrystal_I2C_BitBang which appears to indeed have its own software I2C. That one actually compiles, but the display doesn't react at all to commands (backlight on/off, printing text).