Battery chemistry is actually a lot more complicated than what it may seem. The battery voltage drops under load and recovers slowly when the load decreases, so measuring the voltage under no load or minimal load will give higher voltage compared to the voltage under load, and to make stuff more complicated, an empty batter will have its voltage drop more under load than a full battery, regardless of the initial voltage.
This is why even fully depleted batteries can measure close to 3V after letting them sit idle for long, and then when applying a little load the voltage will dip down. It also takes a while for the voltage to “stabilize” when put under load. With a low load like the tags, this can take days so it’s expected that the voltage will drop relatively rapidly at start and even out soon.
Startup does consume a little more power than the average idling between measurements, but the biggest power consumer is the transmission, so the tag might even start up just fine, but when it tries to transmit, the battery load grows too much and the voltage dips too low.
The random drops you are seeing are relatively “normal”, I’ve noticed there’s a small correlation between those random drops and the way the battery is making contact. After inserting the battery, gently “wiggling” the battery clip on the battery surface reduces the noise slightly but it’s not the only source of that, and in general the “noise” seems to increase as the time goes.