This is a personal view and it may not be valid in all fields, I realize. But my view is that "corresponding author" is a job, not an honor. It is who should be contacted by the editors and later by readers for questions about the paper. With this view, it is best that it be someone with stable contact information, now usually an email address. That suggests that students may not be the best choice if they lose their university email after graduation.
"Principal author" or "first author" in some fields is a completely different concept. In some fields the concepts are foreign and not used.
Principal author, in some fields refers to the PI of a lab. The one that supplies the infrastructure in which research can be done. In some fields they are listed last. In some fields it is interpreted that they had little part in the actual research beyond infrastructure and maybe general guidance. Sadly, in some fields, some interpret this as "this person really did this work and the others are just being carried along".
First author, in some fields, is usually listed first in the ordering of authors on the document and the implication is that they did the majority of the work, perhaps (or not) coming up with the research question and driving the whole project intellectually. Those fields in which first authorship is considered important often have bitter fights over who should be listed first. I find this sad.
In you current situation, however, for purposes of applying for jobs and writing CVs, I suggest that you just add a note at the end that the supervisor insists on being corresponding author (as I think is appropriate). This could short-circuit any feelings that you aren't adequate in some way.
As for grant applications, I think it would be foolish (though I can't rule it out) for those evaluating an application to look at such things and give them weight over what is being proposed in the grant and the information there that backs up the application. Maybe first authorship would give a bit of confidence in those fields in which it is a vital concern.