Escalate, yes, although likely not immediately (there's apparently quite a bit of prep work to get the Leopards, and even more so the Abrams tanks from the USA, up and running smoothly). Spread, no - or at least not to NATO/the EU; I agree with DomesticShortHair that Belarus is already in the middle of it and I always worry about Moldova.
Germany is cautious; they have been throughout this crisis - even before Feb 2022, back to the Russian interventions in Donbas and Crimea. Scholz is newish as Chancellor and inherited a very fragmented situation politically (even Merkel - much more established and connected - was having trouble forming and running a stable coalition government). Germany is an anomoly because of the post-Second World War history and reunification. Among the politicians and the people you've got a segment that are more in the headspace of Poland and the Baltics: very critical (even afraid) of Russia based on experience, but also in different ways cautious about the West/NATO. And then you have the legacy of West Germany: rich and central, but demilitarised for decades, pre-Kosovo, with a complicated recent past in terms of military involvement, and still closely tied militarily to the USA.
Germany is a target: in a ground/naval war, the Baltics, Poland, Finland, Hungary, Romania, Moldova etc. are on the front lines. If something switches to nuclear, though, Germany likely becomes the main target. Putin is probably not crazy and probably won't do anything crazy. But nobody is really sure, and no German politician wants to be the one who took a risk that fucked up everything - even if, realistically, they had no choice.
I'd expect, soon if not already, there will be some narrative from Russia and/or supporters of Russia's war complaining that Germany's actions mean "NATO boots on the ground" in Ukraine to service the new tanks and train Ukrainian forces, and that this is a game changer. It's not. And even if it were: Russian military assets were openly operating as "mercenaries" in Donbas since 2014 if not earlier. NATO isn't doing anything Russia didn't already do, but look out for the disinformation.