How to detect misclasification data after multiclass classification?
Sadly, this isn't possible. Simply put, if you could know for sure that your model made a mistake, then, your model will never make mistakes.
This is the painful reality of deploying models in practice. You will need manual validations to confirm whether your model performed correctly. In some systems, you may be able to outsource this to the user itself (i.e. give them an option to say the model was wrong), but you'll likely want to run independent validation.
Now, there are indeed ways to make this part less painful. First, as you said, you should take a look at the confidence scores. It should indeed be less necessary to verify predictions where the model is highly confident. You should also use your confusion matrix to figure out which predictions are more crucial to verify. Indeed, some mistakes may be less harmful than others.
What you could also do is experiment with building auxiliary binary models that take in the input, the model output, and predicts whether the model made a mistake. This isn't guaranteed to work, but it may give you better confidence scores for your model.