How to edit title/axes of already compiled matplotlib plots

It depends on what aspects of the plot you would like to change. A general solution would be using pickle, based on this related question.

For example, at one point, you could serialize a Figure instance with pickle.dump():

import pickle
import matplotlib.pyplot as plt
import numpy as np

# Plot sine wave as demo
fig = plt.figure()
x = np.linspace(0, 2 * np.pi)
plt.plot(x, np.sin(x))
plt.title("before pickling")

# Save figure to disk
with open("sine.pickle", "wb") as f:
    pickle.dump(fig, f)

Then, at a later point, you could deserialize it using pickle.load() and adjust it as necessary (here, I change the title):

import pickle

with open("sine.pickle", "rb") as f:
    fig_loaded = pickle.load(f)
    
fig_loaded.get_axes()[0].set_title("after pickling")
fig_loaded.show()

Changing other aspects of the Figure is also possible, but will be cumbersome and will imply that you pretty much know the Figure's content. With the given plot, you could for example also change the color of the sine wave after deserialization/loading:

fig_loaded.get_axes()[0].get_lines()[0].set_color("red")

If you need more concrete answers, a more concrete question would be necessary.

In any case, as a caveat, you would need to make sure that the matplotlib version of your Python environment is still the same or a compatible one (on the code level, that is) at the point of deserialization/loading, or otherwise you might see problems like in this question regarding the (de)serialization of plotly instances.