You should use the Matplotlib pane and explicitly pass an axis object to seaborn, i.e.:
import panel as pn
import seaborn
import pandas as pd
import matplotlib.pyplot as plt
pn.extension()
df = pd.DataFrame(np.random.rand(10, 10), columns=[chr(65+i) for i in range(10)], index=[chr(97+i) for i in range(10)])
fig = plt.Figure(figsize=(10, 6))
ax = fig.add_subplot(111)
seaborn.heatmap(df, ax=ax)
pn.pane.Matplotlib(fig)