Conventional current is the total flow of charged carriers.
In an electrolyte, these are both positively and negatively charged ions. In a plasma, electrons and positively charged ions. In ice, it's protons that flow to conduct electricity. In N and P type semiconductors, it's mostly electrons and holes respectively, but in intrinsic (undoped) semiconductors, it's a more even mix. In metals, it's just electrons.
It's rather metal-chauvinistic to concentrate on metals and get uptight about electrons having a negative charge, when there's such a diversity of current conduction mechanisms available, using both negative and positive charge carriers. The pioneers of electrical theory and measurement chose one way, but they could have just as easily picked the other. Then I guess people would have objected to the centres of atoms being negative!
The diode has three junctions in it, metal-N, N-P, and P-metal. Different things happen at each junction, only the middle one is what we'd call a rectifying diode.
Use your favourite search engine to find out how doped semiconductors conduct electricity, and how metals do, and how the junctions work. There's much too much information in those topics for a simple answer here.
The schematic you've shown models at the 'conventional current' level, and is not concerned with what particular charge carriers are involved at various parts of the circuit.