VSE snap a marker to the playhead? Is any easy way to snap a marker to the playhead (green cursor)? (aside from zooming in really far and trying to position it as close as possible)
You can set the Frame of your selected Marker to the current Frame via Python:

import bpy

s = bpy.data.scenes['Scene']

for m in s.timeline_markers:
    if m.select == True:
        m.frame = s.frame_current