DIAGNOSIS This is expected behavior. The monitor's USB-C video input port does not provide significant power output. It delivers just enough to run the monitor itself, not to charge another device.
FIX To charge your Switch while playing, you must use a separate power source for the Switch. Keep the Switch dock's AC adapter plugged into the Switch itself. Alternatively, connect a USB-C power bank directly to the Switch's bottom port while it is connected to the monitor.
IF THAT DIDN'T WORK If your goal is a single-cable solution, it is not possible with this monitor and the Nintendo Switch. The Switch requires a specific power profile (15V) to charge in docked mode, which the monitor's passthrough does not provide.
HEADS UP Using the monitor's second USB-C power input port with a high-power adapter (at least 30W) will power the monitor more efficiently, but it still will not send power back to the Switch. Power flow is one-way: into the monitor.