Short-term shared housing has grown into its own market, so one-to-three-month stays are very doable in most cities, just with different channels and pricing than regular flatshares. The dedicated option is coliving: companies run furnished houses and buildings with private rooms, shared kitchens and workspaces, bills and Wi-Fi bundled, and minimum stays commonly as short as one month. It costs more than a regular room but eliminates deposits negotiations, utility setups, and furniture, which is exactly the friction short-stayers can't amortize. Nomad-heavy cities have plenty; search coliving plus the city name.
The organic option is subletting and interim rooms: tenants who travel or leave mid-lease list their rooms for exactly your kind of duration on flatshare portals and city Facebook groups.
Two cautions particular to short stays: confirm the sublet is permitted, since an unauthorized sublet can unravel under you with little recourse, and keep payments documented and staged monthly rather than lump-summed to someone you just met.