Plugging in wired headset opens Google App and changes volume, nonstop
I procured a second wired headset, and it works with the Maven. However, it does not work with the Galaxy S5.
I got out my multimeter and tested each connection on each headset, and found that they are wired differently. The ZTE Maven and my new headset use the CTIA/AHJ standard, and the Galaxy S5 and my old headset use the OMTP standard. The difference between these two standards is that the ground and microphone connections are swapped.
From Wikipedia (formatting added):

OMTP:

Tip: Left audio

Ring: Right audio

Ring: Microphone

Sleeve: Ground


old Nokia (and also Lumia starting from the 2nd gen), old Samsung (2012 Chromebooks), old Sony Ericsson (2010 and 2011 Xperias), Sony (PlayStation Vita), OnePlus One, X Box One controller with head phone jack, iPhone sold in China
CTIA / AHJ:

Tip: Left audio

Ring: Right audio

Ring: Ground

Sleeve: Microphone


Apple, HTC, LG, Blackberry, latest Nokia (including 1st gen Lumia as well as later models), latest Samsung, Jolla, Sony (Dualshock 4), Microsoft (including Surface and Xbox One controller with chat adapter), most Android phones

My guess is that, when an incorrect headset is used, random noise in the ground connection is sent to the microphone input, which the Galaxy S5 handles gracefully (detects the headset but doesn't receive or transmit any audio) while the Maven does not. This is solved by using a headset of a suitable standard for the given device.