Switzerland is excellent for mtb, bike parks, natural trail/path riding and high level xc. With a fairly long walking season lifts esp cable cars are open longer than in france and the mountain railways run all year.
Ive biked a decent amount around Verbier (outstanding) and above Montreux and a bit further from your chosen area in Lenzerheide/Arosa (more in the Davos part of the country)
Ive hiked in Saint Luc (excellent Hotel Bella Rosa fyi) and skied there and in the very picturesque old villge of Grimentz – we visited again this summer. Ive not biked there but the Guardian featured a high level xc style ride in Saint Luc as one of its “10 best” trails and the Val d’Annivers is very dramatic. If you want something a bit off the beaten track then it could be an interesting option.
Will dig out some more info this evening