In Finland we have these at some restaurants, more often on a fast food places at the kitchen:

Apparently they're more convenient to use for the kitchen staff than a squirt bottle. Fill the thing with ketchup/mustard/mayonnaise and you can 'milk' appropriate amount of whatever on the dish. They're not commonly used by customers, for obvious reasons.

And cheese in coffee is absolutely a thing, but it's not just any cheese, you need to have bread cheese.

I saw them in fairs and public events. It's like a big bottle of condiment with a huge cow tit, like the picture that has been posted here.

I used one while eating my white brattwurst.

They are called "Euterspender" (udder dispenser)

As a Dutchie, I have seen those more in Belgium than in Germany

https://www.nevejan.eu/media/catalog/product/cache/1/image/1800x/eedbff0bcfa2da08a51d078fea91de8d/6/-/6-rack_2.jpg