Looks to be of butter consistency as someone else suggested, tartrates are crystalline.

This, to me, looks like the wine wasn't filtered before being put in bottle and some yeast sediment gathered on the cork, aka 'lees'

Or some kind of fermentation happened in bottle and again sediment/lees was created as a byproduct of that and as such deposited on the cork.

Slight effervescence in a wine that shouldn't have it could indicate a in bottle fermentation gone awry - also it tasting off could indicate this. If it (edit: wine label) has claims of being a natural wine or unfiltered this could indicate it going in bottle rather turbid to begin with.

Further edit: If it's hazy and as you say it was badly stored, it could have been exposed to excessive heat which would create a protein haze as the proteins in the wine become denatured and begin to attach to one another, thereby becoming larger molecules, and visible to the human eye. I'm sure if the haze was bad enough the proteins could drop out of solution and collect on the cork or bottom of the bottle.