Feature importance with high-cardinality categorical features for regression (numerical depdendent variable)
It depends on how you're one-hot encoding them. Many automated solutions for that will name all the converted booleans with a pattern so that a categorical variable called "letter" with values A-Z would end up like:

letter_A, letter_B, letter_C, letter_D,....

If after you've figured out feature importance you've got an array of feature and the associated weight/importance, I would analyze the array and perhaps sum up the feature importance weights for anything starting with "letter%".