The threat isn't directly to invade Germany. It is to stop Germany from intervening when Russia invade it's neighbor countries. EG if you embargo us or provide Military Support to russian opponents, will shut down the power in Germany and you'll freeze to death. A short-term gas disruption will cause Russia to lose some money, but would be much more dangerous for Germany
Russian gas makes up only 1/3rd of Germany's total amount of imported gas and only because it's cheap. If the Russians really were to turn off the valve, the amount could be made up for with other sources. By far not instantly, but nobody would freeze to death, either.
Germany's alleged dependence on Russian gas is mostly a fairytale of US propaganda.
I'm open to the idea that this is overstated, but would love to see the numbers. Is it 1/3rd now or 10 years from now? Does the alternative supply and import infrastructure have the capacity to provide 30% more on short notice? Alternatively, how long and how well can Germany operate with only 60% imports.
It's been around the 35% mark for at least a decade. We also import from Norway (~30%) and the Netherlands (~20%), along with about 6-8% from domestic sources and some imports from the United Kingdom.
The middle east is another potential supplier and Italy, for example, get their gas from Africa. Germany also has the biggest gas storage capacity in Europe and the gas tanks are usually filled quite well before winter (>95%). Not this year though, because the MBAs took a gamble on Nord Stream 2 going operational and lost the wager, resulting in soaring gas prices all across Europe.
You also need to keep in mind that natural gas is not solely used for heating homes, but also industrial processes and generating electricity, among others, which could be reduced or stopped if it really came down to it.
In short: Russia turning off the valves would be more of an inconvenience than the life-threatening situation it is often claimed to be. But personally I don't see that happening, as the Russians have been a very reliable supplier for decades.
There is trade, and then there is giving a geopolitical rival an "off" switch to a sizable percentage of your energy supply.
Free trade requires easy substitutes to remain "free" and opponents of this plan mostly think that energy markets don't work like that because of high switching costs. Germany can not just spin up new nuclear plants or easily buy electricity from neighbors past a certain amount of it's usage. I don't know enough to know if this angle is correct.