Soldering ball and gate valves.Open or closed?

I would think the ball valve open so that the expansion from the heat does not damage the sealing surface. The force distorting the surface over the hole in the ball.

gate valve closed so that there is no tension on the threaded. So as the valve expands and pinches the gate it does not damage the seat.

Some ball valves have resilient seats. Various rubbers and plastics, like PTFE and glass-filled PTFE, can sometimes be present as sealing media. Soldering using a flame can cause their maximum temperatures to be exceeded, and the same is true of welding. Disassembly of the valve to remove these components where present from the heating medium is highly recommended. Stainless steel socket-weld ball valves, for example, are designed to be disassembled for this very reason.

Differential expansion of dissimilar metals within valves when they are strongly heated can cause distortion and loss of performance. In the case of there being no resilient materials present and where the valve can be heated by flame without a risk of deterioration, here's a vote for having the valve partly open during the process out of respect for its internal components.