The Wikipedia article seems pretty good on this topic: https://en.wikipedia.org/wiki/Electricity_sector_in_Germany . You're right, gas has remained pretty steady at about 10 to 15% of electricity generation since the early 2000s. But electricity isn't the only type of energy the country needs, and in the case of gas a much more important use is for space heating. In my opinion, Germany would be in a much better position today if they had increased renewables as they have, but also maintained their nuclear generation, and instead reduced natural gas use for electricity. Then they would have freed up a huge amount of gas to heat buildings, up to 50 TWh-hr per year according to that article, and have lower emissions than they do at present. I think with hindsight, phasing out nuclear power was a big mistake.

In general, nuclear power and renewables mix quite poorly. This is especially relevant for replacing gas, since gas is great at providing variable power (when needed) which neither nuclear power nor (most) renewables are good at. You can also see this move to more variable gas generation by looking at the increased gas power plant install base (https://www.energy-charts.info/charts/installed_power/chart....) without the corresponding increase in generation.

I wouldn't overrate the amount of gas that is freed by nuclear power (also do keep in mind that there is also quite a lot of heat-electricity cogeneration with gas in Germany, which further complicates matters).

If Germany only didn't shut of any nuclear power plants prematurely, then emissions could be reduced significantly since coal would probably be directly replaced. But I doubt the expansion of renewables in Germany would have happened as it did without a parallel nuclear exit in the 2000s. Would it have changed much if the exit in the 2010s didn't happen in terms of renewables? I don't know. But I also think a non-exit would have been politically untenable after Fukushima, with pretty much every party simultaneously being suddenly gung-ho in shutting down nuclear.

I think the phase-out of nuclear, could everything else have stayed the same, was a missed chance. But at the same time western countries which held much more strongly onto nuclear, especially France, are very likely seeing a huge electricity generation issue in the next decades due to very low rates of building nuclear (with huge difficulties) or renewables (not much interest) and a large amount of nuclear power plants going of the grid (https://de.wikipedia.org/wiki/Liste_der_Kernkraftwerke_in_Fr..., the list in the englisch wikipedia unfortunately doesn't include planned closure dates). These dates could (and will) be extended, but as we're seeing right now they're already getting unreliable and nearing the end-of-life.

You can heat houses with other methods than gas, like ground or air heat pumps that use electricity. It might be somewhat complicated though.

Since it's not a drop in replacement, driving this change through might take decades and require changing building legislation etc. I'm unfamiliar what is the situation in the different European countries regarding this, but I know there are EU countries where practically nobody heats with gas.

Building a single house or building around a heating solution is a long term commitment. It might not be easy to change afterwards. This then implicitly makes assumptions about the availability and price of said heating solution.

Politics and national security concerns are inevitable around a large scale energy questions. These things don't "just happen" in a "free market". For example large scale electricity producers or gas suppliers are "too big to fail" and are actively managed by governments.