It's fine. It could be both, Alex. This mixed conditional as you call it is actually the subjunctive mood in English; in fact, what we have here with "I had gone" is the past perfect subjunctive. As I've stated in other posts, the subordinate clauses don't necessarily have to align with what appears to be the tense of the main clause because the main clause is not in a tense at all; it's in a mood.
Now, normally in Modern English, we would put the subordinate clauses in the past tense or past perfect tense so that they align with the aspect of the subjunctive conjugation, but this is not a hard-and-fast rule. Because of this, Harry is basically saying,
"She has told me on many occasions that I am going to die,"
"If I had dropped (subjunctive mood) dead every time that she has
told me that I am going to die, I would (subjunctive mood)
be a medical miracle."
Now, this construction is unnecessary and uncommon in Modern English today; therefore, Harry could just say it this way if he wanted to:
"If I had dropped dead every time that she had told me that I
was going to die, I would be a medical miracle."
This is nothing more than verbal agreement above. It looks better since the past subjunctive and past perfect subjunctive conjugations look exactly like their indicative counterparts except for the simple past subjunctive of "to be", which is always supposed to be "were" for all persons even though native speakers don't always hearken to this rule. In any event, both are correct and mean the same thing. I've written posts on this before when others have asked. See "If you explained what you ___ trying to achieve, I would ...".
Again, this is not common in Modern English anymore, but Harry is obviously showing off his smarts about the subjunctive mood by showing the present perfect tense in the subordinate clause when the past perfect subjunctive is being used in the main clause.
I hope this might have helped you out, Alex. Just know that it's not a very common construction these days, but it is still heard in speech and read in books and articles every so often. Take care and good luck!