Charts do not respond to widget in html when there is more than one plot

I have been successfully using hvplot, holoviews and panel to make some interactive plots in a Jupyter Lab notebook, but I am having troubles when exporting to html.

I am using:

panel 0.13.1
holoviews 1.14.9

If I create a single chart that responds to a widget and export it to html, then all works fine and the chart updates when I change the widget selection. However, if I include more than one plot, then neither plot updates in the resulting html. Is this a known issue, or perhaps there is something else I need to do when there is more than one chart?

As an example, I am using some demo code I found in the panel or holoviews documentation, which is as follows:

import pandas as pd
import numpy as np
import panel as pn


import holoviews as hv
import hvplot.pandas  # noqa: API import


from bokeh.sampledata.iris import flowers

x = pn.widgets.Select(name="x", options=["sepal_width", "petal_width"])
y = pn.widgets.Select(name="y", options=["sepal_length", "petal_length"])

by_species = pn.widgets.Checkbox(name="By species")
color = pn.widgets.ColorPicker(value="#ff0000")

@pn.depends(by_species, color)
def by_species_fn(by_species, color):
    return "species" if by_species else color

plot1 = flowers.hvplot(
    x=x, y=y, kind="scatter", c=by_species_fn, colorbar=False, width=600, legend="top_right"
plot2 = flowers.hvplot(
    x=x, y=y, kind="bivariate", c=by_species_fn, colorbar=True, width=600, legend="top_right"

flower_page = pn.Row(pn.WidgetBox(x, y, color, by_species), plot1, plot2)

This creates a panel with 2 plots and some widgets. In the notebook they both respond to the widgets.
If I create an html output with 1 plot like this:

flower_page = pn.Row(pn.WidgetBox(x, y, color, by_species), plot1)"flower_page.html", embed=True)

then all is fine and the plot responds in the html page (although the color picker doesn’t seem to affect it).
However, if I create the html with both plots:

flower_page = pn.Row(pn.WidgetBox(x, y, color, by_species), plot1, plot2)"flower_page.html", embed=True)

then I find that neither plot responds in the final output.

Am I doing something wrong?