One could say Schloss Elmau – now positioned as a “Luxury Spa Retreat and Cultural Hideaway” – is its proprietor’s personality writ large. “I asked myself what it would take for me to go to a spa,” says Mueller-Elmau, of conceptualising his resort’s new wellness offering. “And what I want is to have a sense of calm, beauty and privacy.”

This meant building a smorgasbord of options so there is a spa experience to suit every guest, whatever their inclination. There are six spas – three for adults and three for families. There are several outdoor infinity pools, including a saltwater pool heated year-round using wood chips and my favourite, an open-air Japanese onsen heated to 40 degrees celsius with splendid mountain views. There are “textile-free” or clothing-optional spas, countless relaxation lounges, steam baths and saunas, one of which is located by a rippling brook.

At 5,400 sqft, the Oriental Hamam is built using 200 million-year-old Bavarian Jurassic stone and purports to be the largest west of Istanbul. It features three large dome rooms with hot stones and water tubs, four treatment rooms, two steam baths and a relaxation area and oriental tea lounge serving Arabic sweets and teas.

Guests can sign up for diverse wellness experiences, including week-long weight-loss regimes to yoga, hiking and mountain biking, spa treatments and chakra-based healing dance. Also available are taijiquan and qigong, as well as Traditional Chinese Medicine (TCM) consultations and strategies led by Imke Konig, Schloss Elmau’s medical spa director and certified TCM doctor.

Many luxury resorts aren’t particularly welcoming to their smallest guests, but this isn’t the case at Schloss Elmau, going by the number of families I see padding past in the resort’s signature sherbet-hued robes. Mueller-Elmau himself has six children, a fact which no doubt parlayed into the resort’s extensive family offerings. The Hideaway’s Family Spa, for instance, has an indoor 25m lap pool, Finnish and herbal saunas, salt steam bath and infrared cabin to warm up quickly after swimming.

Mueller-Elmau says it was his friends who persuaded him to take over the family property instead of migrating to the US as he’d planned.

“They said Schloss Elmau had something no other hotel in the world had – a 100-year-old tradition of having the biggest names in classical music and jazz perform here, without getting a fee.”

Indeed, the world-famous musicians and academics who perform in Schloss Elmau’s wood-beamed concert hall are not paid. Instead they “play to stay” and enjoy the property and its surroundings.

“Many hotels have tried to copy our cultural tradition and failed”, says Mueller-Elmau. “But I invite (the musicians) because I love music. I don’t invite them to fill the hotel or to extend the season.”

Guests are invited to attend performances. One evening, I watched a quintet of young musicians energetically saw away at their violins, before the arrival of a soprano unexpectedly (and to the great delight of the audience) morphs classical into cabaret. Afterward, I pop by the moody Al Camino Jazz Bar, where a visiting professor of music is playing Erroll Garner’s Misty. He’s been coming here since he was a music student, and remarks that the hotel “has some of the best pianos.”

It’s also home to well-stocked libraries and the most impressive hotel bookstore I’ve ever seen, filled with well-curated literature for children and adults alike. No wonder literary greats like Julian Barnes and Ian McEwan have visited. “The whole hotel is designed so that you can read,” says Mueller-Elmau.

Schloss Elmau’s design influences are as worldly as the political summits it hosts. Mueller-Elmau is particularly fond of its Italian-made Catellani & Smith Stchu-Moon lamps, slices of cratered aluminium that throw theatrical pools of light and shadow across the resort’s incarnadine walls. So taken was Mikheil Saakashvili, Georgia’s former president, with the lights that apparently staff had to dismantle 100 of them from the walls so they could fly home with him on his private jet.

Another bestseller (and allegedly the most pilfered) is the hotel’s famous elephant-motif pillow, based on a design Mueller-Elmau discovered in London store, Andrew Martin. “The minute I saw the elephant, I knew that was what I was looking for,” he says, “because the elephant symbolises memory and sound judgement.”

Other notable accents include the animal-skin-like wallcoverings made in Uganda from fig tree bark, as well as the rare, matte-finish Chinese vases made exclusively for the resort by a Shanghainese artisan, using techniques that disappeared some 500 years ago.

Like its spas, the diversity of Schloss Elmau’s restaurants mean guests will be perfectly happy never leaving the resort. Fidelio offers a rotating selection of Japanese and Asian dishes, while Tutto Mondo serves traditional Italian dishes with a modern twist.

A drive up the mountain takes guests to Elmauer Alm, a Bavarian mountain restaurant with stunning views. My pick, however, is Luce d’Oro, Christoph Rainer’s superb two-Michelin-starred Japanese- French restaurant. The relaxed setting belies the sophisticated – and extremely delicious – dishes which cleverly blend French tradition with Asian flavours and techniques. This is fusion at its very best.

But you really should follow Biden and Macron’s lead and head out to the great outdoors. And Schloss Elmau’s fleet of electric BMWs – like the beast of an iX we drove – are available for guests’ complimentary use, perfect for jaunts to nearby Innsbruck, Garmisch-Partenkirchen or Zugspitze, Germany’s highest peak.

I ask Mueller-Elmau whether his ascetic grandfather would approve of the new Schloss Elmau. “He wouldn’t!” exclaims Mueller-Elmau, laughing. “But I’d love to argue with him about it. I don’t like for anyone to feel that they have to do things a certain way. I want total freedom.”

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