You can try this code to apply color to vertices selected in edit mode:

import bpy

def color_to_vertices(color):
    mesh = bpy.context.active_object.data
    bpy.ops.object.mode_set(mode = 'VERTEX_PAINT')

    selected_verts = []
    for vert in mesh.vertices:
        if vert.select == True:
            selected_verts.append(vert)

    for polygon in mesh.polygons:
        for selected_vert in selected_verts:
            for i, index in enumerate(polygon.vertices):
                if selected_vert.index == index:
                    loop_index = polygon.loop_indices[i]
                    mesh.vertex_colors.active.data[loop_index].color = color

import random

RGB = [random.uniform(0,1) for i in range(3)]
color_to_vertices(RGB)

For convenience sake you maybe want to create some panel and an operator.

You can try this code to apply color to vertices selected in edit mode:

import bpy

def color_to_vertices(color):
    mesh = bpy.context.active_object.data
    bpy.ops.object.mode_set(mode = 'VERTEX_PAINT')

    selected_verts = []
    for vert in mesh.vertices:
        if vert.select == True:
            selected_verts.append(vert)

    for polygon in mesh.polygons:
        for selected_vert in selected_verts:
            for i, index in enumerate(polygon.vertices):
                if selected_vert.index == index:
                    loop_index = polygon.loop_indices[i]
                    mesh.vertex_colors.active.data[loop_index].color = color
    
    bpy.ops.object.mode_set(mode = 'EDIT')

import random

RGB = [random.uniform(0,1) for i in range(3)]
color_to_vertices(RGB)

The result will be like this:

Don't forget about proper material node setup if you want to see the result in edit mode (material viewport shading) and render:

For convenience sake you maybe want to create some panel and an operator.