Is considering electron negatively charged just a convention?

Your title and the actual text ask two totally different questions. Which charge we CALL "positive" and which we call "negative" is really just convention. If we would have called the charge of the electron "positive", nothing would have changed, of course.

The reason why the electron charge was called negative is that in the first setups that produced electrical currents, people did not know about the electrons inside the wires as the actual moving particles that carried charge, but thought that the current is realised by ions, therefore they assigned positive charge to these. Until today this convention about electrical current sometimes leads to confusion in which direction current flows inside an electric circuit.

If you would ACTUALLY exchange the charges of electrons and protons, and the charges of all other particles, this would physically correspond to exchanging all particles with their so-called antiparticles. That these exist has been proposed by Paul Dirac and has been experimentally proven since the 1930s many times over. Look here for details.

If you look ONLY at the electromagnetic interaction, theory predicts that the anti-matter counterparts should act the same (if everything is swapped). This is hard to observe, since we, the earth, all planets and most probably all stars and galaxies only consist of matter, while anti-matter on earth is only produced in radioactive decay processes, interactions with cosmic radiation, and in particle experiments. The anti-particles annihilate into photons as soon as they find their corresponding particle or decay after a short time. Therefore we do not see atoms made up of anti-matter in nature. But they are produced in experiments, for example look at The ALPHA experiment at CERN. The experiment so far has found no difference in the spectral lines of anti-hydrogen, which is a positron (anti-electron) bound to an anti-proton, compared to hydrogen. This suggests that chemistry works the same with anti-matter. As a fun fact: At the same cite at CERN it is also tried to find out if anti-matter is influenced by gravity the same way as matter. But this is hard to test. It is of course predicted that gravity is attractive for all (anti-)particles.

Therefore an anti-matter world that would be completely separated from our matter world should work the same way as our world when it comes to everyday physics, including anti-matter smartphones where positrons would circulate inside electric circuits.

Why the world (besides the few exceptions) consists of (what we call) matter and not of (what we call) anti-matter is an open question, since cosmology predicts, if both act the way we understand so far, both should be there in the same amount, while most of it of both should have annihilated into radiation (i.e. photons) early on. This could be a clue that there is a difference between matter and anti-matter that we have not theoretically described yet or already described but not understood yet.

ONE important difference we know is that the weak force, the force that for example causes radioactive beta-decay, actually behaves different for particles and anti-particles. For details of this I would have to write about the quantum mechanical property called spin, which, besides many other things, determines which of the particles and anti-particles participate in weak force interactions, but this probably goes into too much detail. If you want to know more about this look at the WU experiment.

As a small bonus, to be taken with hugh precaution: There recently where suggestions about an idea that the weak force and its interaction with only part of the particles could have lead to evolutionary bias towards the direction in which the DNA helix spins. Without doing any calculations, I think this would suggest that in the anti-matter world the DNA helix would spin the other way around. This is of course very far from being consens so far, but writing the answer reminded of the quoted QUANTA article.