Erratic iOS battery meter and usage from Music app randomly playing on mute
According to the battery meter, your battery appears fine. However, the symptoms you describe are typical of a bad or dying battery. Ideally, you would want to replace the battery with a known-good battery (from another device, for example) to see if the problem persists or not.

In the absence of a known-good battery, one purchased from a reputable supplier can do.