How can I have annotation bboxes above all lines when using multiple axes?

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1

Given the following code:

from pandas import DataFrame, date_range, Timestamp
from numpy import arange

data = DataFrame({'A': arange(100, 200), 'B': arange(500, 400, -1)}, index=date_range('2024-01-01', periods=100))
ax_a = data['A'].plot(color='C0')
ax_b = data['B'].plot(color='C1', secondary_y=True)
ax_a.annotate(
    '', (Timestamp('2024-01-15'), 120), xytext=(Timestamp('2024-03-20'), 120),
    arrowprops=dict(arrowstyle="->", color='C0', ),
)
ax_a.annotate(f'Label A', (Timestamp('2024-03-02'), 120), bbox=dict(fc="0.8"))
ax_b.annotate(
    '', (Timestamp('2024-03-20'), 420), xytext=(Timestamp('2024-01-15'), 420),
    arrowprops=dict(arrowstyle="->", color='C1', ),
)
ax_b.annotate(f'Label B', (Timestamp('2024-02-02'), 420), bbox=dict(fc="0.8"))

I get the following plot:

image

What should I change such that none of the lines, including the annotation arrows, overlap either of the annotation bboxes and their content?

As you can see below, currently any lines plotted on ax_b overlap the bbox for “Label A”.