You're right about the gas reserves in Germany. I watched a documentary recently in which the problem was discussed. Apparently, their tanks are only at 30% at the moment, with, as you state, not much likelihood of them being topped up before the cold weather moves in.
Far more serious is the fact that so much industry in Germany is dependent on gas deliveries. So it's not just the domestic home-heating situation that's causing headaches. The eastern part of the country is in a slightly better position because the majority of communities there are served by locally-sited combined electricity/heating facilities that were originally run on lignite (brown coal) and subsequently converted to gas. However, such plants can be, relatively, easily re-converted should push come to shove.
Whichever way you spin it, though, Germany's going to have to face a tough time in the very near future. In my opinion, that's why they've been so reluctant to step up to the plate and support Ukraine 100% in a sort of tentative appeasement strategy that's gone totally awry.
MsG