From what I have heard the fact that European gas storage is full is nice but not really all that meaningful. The gas storage is only large enough to last a week or something in that magnitude.
(For non German speakers: that linked article's main point is that the gas in German storage may be sent to other European countries, it's not all reserved for the German market.)
As a German, I'm perfectly fine with the reserves serving Europe and not just Germany. Even if/when we run low and have to suffer a bit.
After all, we expect the same from others, that they help us out if they have some and we don't. Energy markets in Europe are connected, for electricity too.