Ask the manufacturer of the sauna.

Can’t directly answer your question. But the best dry sauna I ever experienced was set on a backyard patio of an AirBnB in New Zealand. It was just steps from the back door. If you install one outside, you can take it with you when/if you move.

If it's a free-standing unit, the exterior faces of the sauna walls will definitely warm-up the space. Another detail is the outlet vent. If the used air inside the sauna is evacuated into the bathroom, that's an additional source of heat. It all depends on the specs and the designated space.

The heat doesn’t stay in the unit. Thermodynamics. Or it would always be hot. It leaks out over time. Some faster. Some slower. Depends on the insulation and sealing. The faster leakers make your bath hot. All add to the burden of your HVAC in summer, but help heat in winter.