There may be more elegant ways. But the following suggestion sets up buttons with args for all colors available to go.Heatmap() by default by building one figure for every colorscale, "stealing" those colorscales one by one, and then making them available as updates to your figure throgh:

# buttons, temporary figures and colorscales
for i, scale in enumerate(scales):
    colors.append(go.Figure(data=go.Heatmap(z=z,colorscale = scale)).data[0].colorscale)
    buttons.append(dict(method='restyle',
                        label=scale,
                        visible=True,
                        args=[{'colorscale':[colors[i]],
                                }, ],
                        )
                  )

Figure with update button:

Some details about the solution:

So why the hassle with colors.append(go.Figure(data=go.Heatmap(z=z,colorscale = scale)).data[0].colorscale)? As I said, there might be more elegant ways. But this approach at least ensures that the colorscales keep the same sructure for all colors in:

(Heatmap({
     'colorscale': [[0.0, 'rgb(237, 229, 207)'], [0.16666666666666666, 'rgb(224,
                    194, 162)'], [0.3333333333333333, 'rgb(211, 156, 131)'], [0.5,
                    'rgb(193, 118, 111)'], [0.6666666666666666, 'rgb(166, 84, 97)'],
                    [0.8333333333333334, 'rgb(129, 55, 83)'], [1.0, 'rgb(84, 31,
                    63)']],
     'z': [[1, 20, 30], [20, 1, 60], [30, 60, 1]]
 }),)

Which is the structure you're editing through buttons and updatemenu.

Complete code:

# imports 
import plotly.graph_objects as go

# data
z=[[1, 20, 30],
  [20, 1, 60],
  [30, 60, 1]]

# every colorscale available to go.Heatmap() by default
scales =     ['aggrnyl', 'agsunset', 'algae', 'amp', 'armyrose', 'balance',
             'blackbody', 'bluered', 'blues', 'blugrn', 'bluyl', 'brbg',
             'brwnyl', 'bugn', 'bupu', 'burg', 'burgyl', 'cividis', 'curl',
             'darkmint', 'deep', 'delta', 'dense', 'earth', 'edge', 'electric',
             'emrld', 'fall', 'geyser', 'gnbu', 'gray', 'greens', 'greys',
             'haline', 'hot', 'hsv', 'ice', 'icefire', 'inferno', 'jet',
             'magenta', 'magma', 'matter', 'mint', 'mrybm', 'mygbm', 'oranges',
             'orrd', 'oryel', 'peach', 'phase', 'picnic', 'pinkyl', 'piyg',
             'plasma', 'plotly3', 'portland', 'prgn', 'pubu', 'pubugn', 'puor',
             'purd', 'purp', 'purples', 'purpor', 'rainbow', 'rdbu', 'rdgy',
             'rdpu', 'rdylbu', 'rdylgn', 'redor', 'reds', 'solar', 'spectral',
             'speed', 'sunset', 'sunsetdark', 'teal', 'tealgrn', 'tealrose',
             'tempo', 'temps', 'thermal', 'tropic', 'turbid', 'twilight',
             'viridis', 'ylgn', 'ylgnbu', 'ylorbr', 'ylorrd']

# scales = scales[10:13]
colors =[]
buttons = []

# buttons, temporary figures and colorscales
for i, scale in enumerate(scales):
    colors.append(go.Figure(data=go.Heatmap(z=z,colorscale = scale)).data[0].colorscale)
    buttons.append(dict(method='restyle',
                        label=scale,
                        visible=True,
                        args=[{'colorscale':[colors[i]],
                                }, ],
                        )
                  )

# Initial figure:
fig = go.Figure(data=go.Heatmap(z=z, colorscale = scales[0]))

# some adjustments to the updatemenus
updatemenu = []
your_menu = dict()
updatemenu.append(your_menu)
updatemenu[0]['buttons'] = buttons
fig.update_layout(showlegend=False, updatemenus=updatemenu)

# f = fig.
fig.show()

You will need to manually insert a colour scale

trace = go.Heatmap(z=probability_matrix, colorscale=[[0.0, '#F5FFFA'], 
                         [0.2, '#ADD8E6'], 
                         [0.4, '#87CEEB'],
                         [0.6, '#87CEFA'], 
                         [0.8, '#40E0D0'], 
                         [1.0, '#00CED1']])
data=[trace]

You can use zmin and zmax parameters of go.Heatmap.

The code you use to generate a color palette works just fine. You only need to provide data that match with a heatmap. The following code provides this:

library(RColorBrewer)
library(plotly)

# your palette definition
palette <- colorRampPalette(c("darkblue", "blue", "lightblue1",
                              "green","yellow", "red", "darkred"))

set.seed(9876)    # for reproducibility

## a complete random set
hmdata <- matrix(data = sample(x = 1:10^6, size = 100*100), nrow = 100, ncol = 100)
plot_ly(z = hmdata, colors = palette(50), type = "heatmap")

This gives the following heatmap:

## a random set that has been sorted
hmdata_s <- matrix(data = sort(sample(x = 1:10^6, size = 100*100)), nrow = 100, ncol = 100)
plot_ly(z = hmdata_s, colors = palette(50), type = "heatmap")

Yielding this plot:

Please let me know whether this is what you want.

UPDATE

you can set custom scale in plot_ly with zauto, zmax, and zmin. The following 2 pieces of code and graphs will illustrate this:

The scale is set from 1 to 100 and the data vary similarly:

hmdata_s3 <- matrix(data = sort(sample(x = 1:100, size = 100*100, replace = TRUE)), nrow = 100, ncol = 100)
plot_ly(z = hmdata_s3, colors = palette(50), type = "heatmap", zauto = FALSE, zmin = 1, zmax = 100)

The scale is set from 1 to 100 and the data vary between 50 and 100 only

hmdata_s4 <- matrix(data = sort(sample(x = 50:100, size = 100*100, replace = TRUE)), nrow = 100, ncol = 100)
plot_ly(z = hmdata_s4, colors = palette(50), type = "heatmap", zauto = FALSE, zmin = 1, zmax = 100)