I love this term (though I don’t appreciate its sonic impacts). It’s used to describe an unnatural emphasis on some higher frequencies some of the time.
It is typically associated with solid-state amplification gear.
We rarely ever use the term to describe the performance of a loudspeaker. Here, we would say it’s bright or has a glare to the sound.
Over-etched seems to track along with the music as if it were added as opposed to inherent.
Why would this matter?
Because the causes of over-etching are typically dynamic distortion products generated by specific combinations of frequency or amplitude events. We know this because once identified by competent circuit designers it can be reduced or eliminated through changes in the basic circuitry topology.
For example, it is not uncommon to experience over-etching in high feedback circuits yet extremely rare (or non-existent) in zero or low feedback topologies.
Segregating the differences between bright and glare vs. over-etched can be a real key to the circuit designer of audio equipment.