The name of Germany’s beleaguered chancellor, Olaf Scholz, was not on the ballot on Sunday, as his home state of Brandenburg went to the polls. But it might as well have been. Approval ratings for the coalition of Social Democrats, Greens and liberals that he leads have plunged to record lows. Earlier this month, a far-right party shockingly won a regional election for the first time since the second world war. Had Alternative für Deutschland (AfD) repeated that feat in Brandenburg – an eastern state that Mr Scholz’s Social Democratic party (SPD) has controlled since reunification – the knives would have been out for a leader whose party fears a rout in federal elections next year.

In the event, disaster was averted. By a narrow margin, the AfD finished second, not first, as the SPD benefited from tactical voting to keep it at bay. But the good news for the chancellor ends there. Even allowing for the particular political dynamics of eastern Germany, a dismal September for the coalition government risks holing it below the waterline. In elections in Brandenburg, Saxony and Thuringia, the Greens struggled even to reach the 5% threshold necessary for parliamentary representation. The liberal Free Democratic party (FDP) was all but extinguished from the political map. In Brandenburg, the long-serving SPD state premier, Dietmar Woidke, retained office only after effectively disassociating himself from the national party and Mr Scholz.

The upshot of these humiliations is likely to be a dysfunctional, fractured administration at war with itself, ahead of next year’s political reckoning. The coalition partners will posture and seek to blame each other for the mess they find themselves in. In the absence of an internal party push to replace him, which remains possible, Mr Scholz will continue to be a convenient punchbag and scapegoat.

This spectacle of progressive disarray is deeply troubling at a time when the EU’s most powerful member state is confronting major societal, environmental and geopolitical challenges. The ongoing rise of the Putin-friendly AfD – and the parallel success of a startup “left-conservative” party with roots in the east – is generating new levels of opposition both to the pace of the green transition and to continued support for Ukraine’s struggle against Russia. The cost of living crisis is being relentlessly weaponised by the far right for its own ends, as it seeks to demonise migrants as a drain on scarce resources. And in the face of Chinese and American competition, job losses and factory closures are being mooted by Germany’s car manufacturers.

It is hard to envisage a disunited and demoralised government operating effectively on these multiple and threatening fronts. From the outset, Mr Scholz’s “traffic light” coalition has been undermined by division and disagreement. Crucially, the FDP finance minister, Christian Lindner, a fiscal hawk, has steadfastly refused to license the sort of public investment needed to alleviate anxieties in an age of insecurity.

That has allowed the AfD to make the political weather on themes such as immigration. Chillingly, in Brandenburg – where its regional party has been judged particularly extreme by domestic intelligence agencies – the AfD came first in every voting cohort under the age of 60. By a whisker, Mr Scholz’s party won a regional vote on Sunday that doubled as an unofficial referendum on his government. But after a tumultuous month, it feels like a pyrrhic victory.