It doesn’t take long for the startling three-guitar masterclass that is Wilco to power up. The feted Chicago band – recipients of a Grammy and, latterly, soundtrackers of TV chef drama The Bear – edge in sideways, with just a brief electric guitar exchange on tonight’s set opener, Hell Is Chrome.

Soon, though, the promise of the three old-school Persian rugs arrayed on the floor, and the banks of effects pedals laid on top, is made good. Handshake Drugs boasts all the fun of the Wilco fair. (At least, as far as the music is concerned; lyrically, this a sad, elliptical tale about singer Jeff Tweedy scoring at the height of his former addiction to painkillers.)

Lanky electric guitarist Nels Cline holds court on the left, alternating between curt flurries and succinct peals. Tweedy takes up the call centre stage; multi-instrumentalist Pat Sansone chimes in from the right. Their guitar triple helix is nimble and engrossing, rather than cliched or indulgent. By the end, the band invent a fourth sound: a sour foghorn cry they hold at length before dropping away into a gully of reverent silence.

So very many deaths have been foretold for the guitar band. But Wilco – nearly 30 years old as a unit – have seen them all off. Every few years their appeal renews. New fan blood has arrived via their four songs on The Bear, one of them – Spiders (Kidsmoke) – used twice, the first time to soundtrack the famed one-shot kitchen nervous breakdown in series one, episode seven.

Demographically, Wilco inevitably skew dadwards. We are, though, surely long past the point of equating trips around the sun with cosiness; the band are very much about the interplay of comfort and discomfort. Younger artists routinely rate them, too. Bedroom pop producer Jay Som, who moonlights as the touring bassist for supergroup Boygenius, has hymned the Wilco song Impossible Germany, for its use of the axis powers as a metaphor for failed communication. A regular presence in Wilco’s sets, Impossible Germany tonight foregrounds Cline, whose improvised pileup of banshee notes is lit by strobes. “Exactly how it was written,” observes Tweedy drolly at the end.

There is much to look up to in Wilco, survivors who have cracked the code of success on their own terms. They regularly release inventive yet hummable work that taps sufficient canonical cornerstones – the Beatles, the Band – to garner a sizeable audience. Tweedy’s productivity means that as well as publishing his third book this autumn, Wilco have a new record coming – Cousin, out at the end of the month. (“Nothing to do with The Bear!” insists Tweedy: “cousin” is a word much-bandied on the show). Its teaser is Evicted, a pretty heartbreak ballad that boasts shades of Prince’s Raspberry Beret as played by Teenage Fanclub.

This tour, however, foregrounds Cruel Country, Wilco’s all-in-a-room, state-of-the-American-nation album of last year. I Am My Mother is just one of its highlights, expressing dismay at the US reception of migrants at its southern border. Cruel Country found this restless band circling back to their Americana roots – associations they had shaken loose across several albums.

Having co-founded Wilco as a country-leaning rock band, Tweedy eventually chafed at those restrictions. As the millennium turned, the band made an album, Yankee Hotel Foxtrot (released in 2002), that veered into more experimental territory. (Radiohead did a similar thing with 2000’s Kid A, swapping prog indie for silvery electronics.) Not all Wilco members were keen. Their label dropped them. The band responded by streaming YHF on their website – finding another label, and critical acclaim, in the process.

Only Tweedy and bassist John Stirratt remain of the original lineup. But this Wilco iteration has been solid since 2004, when virtuoso guitarist Cline came in to sprinkle even more avant garde fairy dust all over their mutating offering. Now, Wilco’s records come out on their own label, dBpm, answering to no suit.

Theirs has been a hard-won state of grace; the fact that Wilco have outlived substance abuse, genre wars, business wrangling and the death of one of their former members, Jay Bennett, from an accidental fentanyl overdose, means that when Tweedy sings, it’s worth listening. His work can seem easygoing, but it is literary and emotionally complex. Tonight is as much about a body of work ostensibly themed around overcoming as it is about searching guitar fireworks.

“I am an American aquarium drinker, I assassin down the avenue,” runs the opening to one of Wilco’s greatest songs, I Am Trying to Break Your Heart. (Tonight, it features short breakdowns – a nod, seemingly, to the alcoholism Tweedy once wrestled with; drummer Glenn Kotche and keys player Mikael Jorgensen get their turn to shine.)

Over the course of this gig, Wilco consistently combine familiarity with startling sonics, and challenge with succour. “Jeff is our great, wry, American consolation poet,” wrote the Booker-winning author George Saunders in the liner notes for one of Tweedy’s solo albums, attesting to his band’s skill at processing difficulty and refashioning it as classic guitar fireworks.