[Bug]: Contour segments changed after clabel

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### Bug summary

`ax.clabel` changes the contour segments itself as it removes the label part of the contours.

Python 3.11.8 + Matplotlib 3.7.1 doesn't change the contour itself, where as Python 3.11.9 + Matplotlib 3.9.1 changes it. Is this an intended change?

### Code for reproduction

```Python
import numpy as np
import matplotlib.pyplot as plt

size = 1000
sigma_x = 1.
sigma_y = 1.

x = np.linspace(-3, 3, size)
y = np.linspace(-3, 3, size)

xx, yy = np.meshgrid(x, y)
z = (1/(2*np.pi*sigma_x*sigma_y) * np.exp(-(xx**2/(2*sigma_x**2)
+ yy**2/(2*sigma_y**2))))

extent = [x[0], x[-1], y[0], y[-1]]
fig, ax = plt.subplots()
ax.imshow(z, extent=extent)
cs = ax.contour(z, extent=extent, colors='w')
seg1 = cs.allsegs[3][0]
ax.clabel(cs, cs.levels, fmt='%.5f%%', fontsize=15)
seg2 = cs.allsegs[3][0]
plt.show()

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(6, 3))
ax1.plot(seg1[:, 0], seg1[:, 1], marker='.', ms=1)
ax1.set_title('Before ax.clabel')
ax2.plot(seg2[:, 0], seg2[:, 1], marker='.', ms=1)
ax2.set_title('After ax.clabel')
plt.show()
```

### Actual outcome

Contour segments changed after `ax.clabel`. The labeled part is removed from the contour

### Expected outcome

Keep the contour segment unchanged

### Additional information

Python 3.11.8 + Matplotlib 3.7.1 doesn't change the contour itself, where as Python 3.11.9 + Matplotlib 3.9.1 changes it. Is this an intended change?

### Operating system

MacOS

### Matplotlib Version

3.9.1

### Matplotlib Backend

_No response_

### Python version

3.11.9

### Jupyter version

_No response_

### Installation

None

Start with the provided Python reproduction and the ax.clabel entry point, comparing Matplotlib 3.7.1 and 3.9.1 behavior. Inspect how contour segments are represented before and after labeling. Done means determining whether the changed segments are intentional and, if not, preserving the original contour segment while still displaying the label.

Written by the indexing model from the issue text.