plotly figure subplot grid lost after converting back from JSON

Describe your context

dash==2.8.1
dash-bootstrap-components==1.4.0
dash-core-components==2.0.0
dash-extensions==0.1.13
dash-html-components==2.0.0
dash-leaflet==0.1.23
dash-table==5.0.0
plotly==5.13.1

Describe the bug
I am trying to update a plotly figure containing subplots within a dash callback but get the error "Exception: Use plotly.tools.make_subplots to create a subplot grid".

The Figure object is passed as a State to the callback function. Because the figure is passed to the callback function as a dict, I use fig =pio.from_json(json.dumps(fig)) to convert it back to a proper Figure object. However, after conversion, this Figure object does not seem to know about its subplots anymore, raising the following exception whenever I try to reference anything subplot-related, e.g. fig.print_grid() or fig.add_trace([...], row=2, col=1):

Exception: Use plotly.tools.make_subplots to create a subplot grid

Minimal code to reproduce:

fig = plotly.subplots.make_subplots(
    rows=3, 
    cols=1,
)
fig.print_grid()     # this works fine
fig2 = pio.from_json(fig.to_json()) # convert to json and back
fig2.print_grid()   # this raises an Exception

Full example app:

import json
from dash import Dash, html, dcc, Input, Output, State, callback_context
import plotly.graph_objects as go
import plotly.io as pio
import plotly.subplots

app = Dash(
    name=__name__,
    title="Test app",
)

# create the initial empty figure
fig = plotly.subplots.make_subplots(
    rows=3,
    cols=1,
)

# create the layout
app.layout = html.Div(children=[
    html.Button("Test me", id="button"),
    dcc.Graph(id="graph", figure=fig)
])


@app.callback(
    Output("graph", "figure"), 
    Input("button", "n_clicks"), 
    State("graph", "figure"),
    prevent_initial_call=True
)
def update_graph(n_clicks, figure):
    # update the figure
    figure = pio.from_json(json.dumps(figure))
    
    figure.print_grid() # this raises an Exception
    
    figure.add_trace(
        go.Scatter(
            x=[0, 1, 2, 3],
            y=[10, 20, 10, 0],
            name=f"line",
        ),
        row=2,
        col=1,
    ) # this also raises an Exception

    return figure


if __name__ == "__main__":
    app.run_server(debug=True)

Expected behavior
I expect to be able to access the subplots of the figure in the callback method.

Start with the minimal reproduction in the issue, especially make_subplots(), pio.from_json(), and the Dash callback that receives figure state. Trace how subplot information is represented through JSON conversion, then verify the fix by ensuring print_grid() and add_trace(..., row=2, col=1) work after conversion.