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.
Full capacity is ~1000TWh[0], while winter monthly consumption is around 450 TWh[1].
In other words, way more than a week, and yes, the storage does make a meaningful difference.
[0]: https://www.statista.com/statistics/1294025/quarterly-gas-in...
[1]: https://energy.ec.europa.eu/system/files/2022-04/Quarterly%2...
Some other European countries have enough gas storage for months - the Netherlands has 123 days of gas stored [1]
[1] https://www.energylivenews.com/2022/10/31/uk-has-nine-days-o...
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.
A picture: https://old.reddit.com/r/hardenergy/comments/2d4sgy/natural_...