KernelDensity incorrect handling of bandwidth

### Describe the bug

I was using kernel density estimator
https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KernelDensity.html
using 'silverman' or 'scott' as the bandwidth argument. Then I found that the bandwidth automatically adjusted by the algorithm is independent of the actual scale of the dataset. In fact, I was shocked to find that the calculation of a bandwidth in https://github.com/scikit-learn/scikit-learn/blob/main/sklearn/neighbors/_kde.py for 'silverman' and 'scott' does not check the scales of data at all. 

Suppose I fit the model `kde` to some 2D data `X` and get the bandwidth as `kde.bandwidth_`.
Next, I fit the model `kde` to the same 2D data `X` but with all elements multiplied by, say, 20 and get the bandwidth as `kde.bandwidth_`. 
I found that these two values of `kde.bandwidth_` are equal (it is calculated from the shape of `X`, see the source code). But obviously they should differ by a factor of 20 if the bandwidth is really computed in a truly adaptive manner.

For your reference, I want to mention that scipy's KDE https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.gaussian_kde.html calculates the covariance of data to extract the scale of data. I think this is the right thing to do.

Note that if the bandwidth is incorrect, everything else is incorrect too, including probablities of samples, etc.

### Steps/Code to Reproduce

```python
import numpy as np
from sklearn.neighbors import KernelDensity
X = np.random.randn(1000, 2)
kde = KernelDensity(bandwidth='scott')
kde.fit(X)
print(kde.bandwidth_)

kde.fit(X * 20)
print(kde.bandwidth_)
```

### Expected Results

Different bandwidths for data sets with different scales.

### Actual Results

0.31622776601683794
0.31622776601683794

### Versions

```shell
1.2.1
```

COMMENT:
One can visually see the sickness of the current implementation by running the code below. The resulting plot is shown at the bottom. I'm using "silverman" here but a similar result is obtained with "scott" too.
@glemaitre @jovan-stojanovic

```python
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm
from sklearn.neighbors import KernelDensity

N = 200
np.random.seed(1)

X = np.concatenate(
    (np.random.normal(0, 5, int(0.3 * N)), np.random.normal(15, 5, int(0.7 * N)))
)[:, np.newaxis]

X_plot = np.linspace(-15, 30, 1000)[:, np.newaxis]

true_dens = 0.3 * norm(loc=0, scale=5).pdf(X_plot[:, 0]) + 0.7 * norm(loc=15, scale=5).pdf(X_plot[:, 0])

fig, ax = plt.subplots()
ax.fill(X_plot[:, 0], true_dens, fc="black", alpha=0.2, label="input distribution")

colors = ["navy", "cornflowerblue", "darkorange"]
kernels = ["gaussian", "tophat", "epanechnikov"]
lw = 2

for color, kernel in zip(colors, kernels):
    kde = KernelDensity(kernel=kernel, bandwidth="silverman").fit(X)
    log_dens = kde.score_samples(X_plot)
    ax.plot(
        X_plot[:, 0],
        np.exp(log_dens),
        color=color,
        lw=lw,
        linestyle="-",
        label="kernel = '{0}'".format(kernel),
    )

ax.legend(loc="upper left")
ax.plot(X[:, 0], -0.005 - 0.01 * np.random.random(X.shape[0]), "+k")

plt.show()
```

Update: I replaced a link to the plot with direct embedding for better readability.

<img src="https://user-images.githubusercontent.com/52037101/220235906-b796a312-4a1b-4884-82df-390500d5d578.png" width="512"/>

Labels: Bug, module:neighbors