how do you insert statistical annotations in a seaboarn figure level plot or catplot?

I think you can just iterate over the axes in the FacetGrid and apply the Annotator element wise.

Here is a short example with your provided code:

import seaborn as sns
from statannotations.Annotator import Annotator
%matplotlib inline


tips = sns.load_dataset("tips")

args = dict(x="sex", y="total_bill", data=tips, hue="smoker", hue_order=["Yes","No"], order=['Male', 'Female'])

g = sns.catplot(edgecolor="black", errcolor="black", errwidth=1.5, capsize = 0.1, height=4, aspect=.7,alpha=0.5, kind="bar", ci = "sd", row="time", **args)
g.map(sns.stripplot, args["x"], args["y"], args["hue"], hue_order=args["hue_order"], order=args["order"], palette=sns.color_palette(), dodge=True, alpha=0.6, ec='k', linewidth=1)

pairs = [
    (("Male", "Yes"), ("Male", "No")),
    (("Female", "Yes"), ("Female", "No"))
]

for ax_n in g.axes:
    for ax in ax_n:
        annot = Annotator(ax, pairs, **args)
        annot.configure(test='Mann-Whitney', text_format='simple', loc='inside', verbose=2)
        annot.apply_test().annotate()

This produces the following plot: