Nonlinear colormap in a folium map

I'm drawing colored regions on a folium map using log scale shading. Using custom colormap, the region colors seem to be ok. But the colormap, when added to the map legend, still looks linear:

Is there any way to draw it as equal-width colored rectangles with text values underneath?

import numpy as np, branca, folium
m = folium.Map()
colormap = branca.colormap.LinearColormap(colors=['blue', 'green', 'yellow', 'orange', 'red'],
                                          index = np.round(np.exp(np.linspace(0, 9, 5))),
                                          vmin = 0, vmax = np.exp(9),
           ).to_step(n=6, index=np.round(np.exp(np.linspace(0, 9, 6))))
colormap.add_to(m)

There is no Folium-native way to do this, and branca legends seem to be resistant to custom scaling. A workaround I have found is to create the legend separately (I use matplotlib), then overlay it on the Folium map as a Custom Icon. Looks like this:

import matplotlib.pyplot as plt
import matplotlib.lines as mlines
import numpy as np
import folium
from folium.features import CustomIcon
import matplotlib.colors as mcolors

def generate_legend(num_colors):
    # dynamically generate a color map
    cmap = plt.get_cmap('viridis', num_colors)
    colors = [cmap(i) for i in range(cmap.N)]
    
    # generate labels based on how many colors there are
    log_labels = np.logspace(0, num_colors, num=num_colors, base=10).astype(int)
    
    fig, ax = plt.subplots(figsize=(6, 0.6))
    font_size = 12
    line_width = 30 
    
    # create colors
    for i, color in enumerate(colors):
        plt.plot([i, i+1], [1, 1], color=color, solid_capstyle='butt', linewidth=line_width)
        plt.text(i+0.5, 0.5, f'{log_labels[i]}', ha='center', va='center', fontsize=font_size, transform=ax.transData)

    ax.set_xlim(0, num_colors)
    ax.set_ylim(0, 2)
    ax.axis('off')
    plt.subplots_adjust(left=0, right=1, top=1, bottom=0, wspace=0, hspace=0)
    plt.savefig('dynamic_legend.png', dpi=300, transparent=True, bbox_inches='tight', pad_inches=0)
    plt.close()

    # add legend to map
    m = folium.Map(location=[20, 0], zoom_start=2)
    legend_img = 'dynamic_legend.png'
    icon = CustomIcon(legend_img, icon_size=(600, 120))  # Adjust icon size as needed

    marker = folium.Marker(location=[-25, 0], icon=icon, popup='Legend')  # Adjust location as needed
    m.add_child(marker)

    m.save('map_with_dynamic_legend.html')

num_colors = 5  
generate_legend(num_colors)