ycb_matplotlib_pr25332

what a new run launched now would send

[Bug]: Unable to pickle figure with aligned labels
### Bug summary

 Unable to pickle figure after calling `align_labels()`

### Code for reproduction

```python
import matplotlib.pyplot as plt
import pickle

fig = plt.figure()
ax1 = fig.add_subplot(211)
ax2 = fig.add_subplot(212)
time=[0,1,2,3,4]
speed=[40000,4300,4500,4700,4800]
acc=[10,11,12,13,14]
ax1.plot(time,speed)
ax1.set_ylabel('speed')
ax2.plot(time,acc)
ax2.set_ylabel('acc')

fig.align_labels() ##pickling works after removing this line 

pickle.dumps(fig)
plt.show()
```


### Actual outcome
```
align.py", line 16
pickle.dumps(fig)
TypeError: cannot pickle 'weakref.ReferenceType' object
```
### Expected outcome

Pickling successful

### Additional information

_No response_

### Operating system

Windows

### Matplotlib Version

3.7.0

### Matplotlib Backend

_No response_

### Python version

_No response_

### Jupyter version

_No response_

### Installation

None

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