How to add control for single subplot in plotly?

Unfortunately, this is not a complete answer. But hopefully, what I'm about to show you will help you on your way. You see, you can specify which subplot to edit by the traces contained in that subplot. You do so by adding an integer in args() like so:

buttons=list([
    dict(
        args=["type", "surface", [2]],
        label="3D Surface",
        method="restyle"
    )

And [2] references the position of your trace in fig.data:

(Scattergeo({
     'geo': 'geo',
     'hoverinfo': 'text',
     'lat': array([ 34.5  , -23.3  ,  14.501, ...,  15.05 ,  14.02 ,  34.8  ]),
     'lon': array([ 131.6  ,  -67.62 ,  -90.876, ...,   42.18 ,   42.75 , -108.   ]),
     'marker': {'color': 'crimson', 'opacity': 0.8, 'size': 4},
     'mode': 'markers',
     'showlegend': False
 }),
 Bar({
     'marker': {'color': 'crimson'},
     'showlegend': False,
     'x': array(['United States', 'Russia', 'Indonesia', 'Japan', 'Chile', 'Ethiopia',
                 'Papua New Guinea', 'Philippines', 'Mexico', 'Iceland'], dtype=object),
     'xaxis': 'x',
     'y': array([184, 169, 136, 111,  87,  57,  54,  49,  41,  38], dtype=int64),
     'yaxis': 'y'
 }),
 Surface({
     'scene': 'scene',
     'showscale': False,

The problem is, that doing it this way in your case will trigger some very peculiar behavior: when the button is set to heatmap, the data becomes bart of the Bar figure:

And what's even stranger, is that it looks the way it should when you select 3D Surface again:

And I honestly have no idea what causes this. Take a look for yourself in the complete code snippet below and see what you can make of it. Maybe we'll be able to figure it out eventually...

Complete code:

from plotly.subplots import make_subplots
import plotly.graph_objects as go

import pandas as pd

# read in volcano database data
df = pd.read_csv(
    "https://raw.githubusercontent.com/plotly/datasets/master/volcano_db.csv",
    encoding="iso-8859-1",
)

# frequency of Country
freq = df
freq = freq.Country.value_counts().reset_index().rename(columns={"index": "x"})

# read in 3d volcano surface data
df_v = pd.read_csv("https://raw.githubusercontent.com/plotly/datasets/master/volcano.csv")
df_v

fig = make_subplots(
    rows=3,
    cols=2,
    column_widths=[0.6, 0.4],
    row_heights=[0.4, 0.2, 0.4],
    specs=[
        [{"type": "scattergeo", "rowspan": 2}, {"type": "bar"}],
        [None, None],
        [None,                                 {"type": "surface"}]
    ]
)

# Add scattergeo globe map of volcano locations
scatter_geo = go.Scattergeo(
    lat=df["Latitude"],
    lon=df["Longitude"],
    mode="markers",
    hoverinfo="text",
    showlegend=False,
    marker=dict(color="crimson", size=4, opacity=0.8)
)

fig.add_trace(
    scatter_geo,
    row=1,
    col=1
)

# Add locations bar chart
bar = go.Bar(
    x=freq["x"][0:10],
    y=freq["Country"][0:10],
    marker=dict(color="crimson"),
    showlegend=False
)

fig.add_trace(
    bar,
    row=1,
    col=2
)

# Add 3d surface of volcano
surface_3d = go.Surface(
    z=df_v.values.tolist(),
    showscale=False
)

fig.add_trace(
    surface_3d,
    row=3,
    col=2
)

# Add dropdown

updatemenu = dict(
    buttons=list([
        dict(
            args=["type", "surface", [2]],
            label="3D Surface",
            method="restyle"
        ),
        dict(
            args=["type", "heatmap", [2]],
            label="Heatmap",
            method="restyle"
        )
    ]),
    direction="down",
    pad={"r": 10, "t": 10},
    showactive=True,  
    x=1,
    y=0.4
)

fig['layout'].update(
    updatemenus=[{}, {}, {}, {}, {}, updatemenu]
)

#Add slider

steps = []
for i in range(10):
    step = dict(
        method="update",
        args=[{"title": "Slider switched to step: " + str(i)}],  # layout attribute
    )
    steps.append(step)
    
slider = dict(
    active=10,
    currentvalue={"prefix": "Frequency: "},
    pad={"t": 50},
    steps=steps
)

fig.update_layout(
    sliders=[slider]
)

# Update geo subplot properties
fig.update_geos(
    projection_type="orthographic",
    landcolor="white",
    oceancolor="MidnightBlue",
    showocean=True,
    lakecolor="LightBlue"
)

# Rotate x-axis labels
fig.update_xaxes(tickangle=45)

# Set theme, margin, and annotation in layout
fig.update_layout(
    autosize=False,
    width=800,
    height=500,
    template="plotly_dark",
    margin=dict(r=10, t=25, b=40, l=60),
    scene_camera_eye=dict(x=2, y=2, z=0.3),
    annotations=[
        dict(
            text="Source: NOAA",
            showarrow=False,
            xref="paper",
            yref="paper",
            x=0,
            y=0)
    ]
)
fig.show()