How to handle performance degradation due to domain transfers in data
There are multiple ways to detect covariate shift, for example Kullback–Leibler divergence but my favorite is adverserial validation. For images I would also look at the shap explainer, if its activating on different random places in the test set, you can suspect something fishy in concept.

Remedy concept shift with NN- try batch normalization if you havent. Why? Weights of the deeper layer, learned by the neural net, will be relatively less dependent on the weights learned on the shallower layer, hence avoiding shift.