What is the ruling on moving between mosques on Fridays, abandoning the local mosque with the intention of seeking sermons that are more beneficial?

There is no objection to choosing a more distant mosque for Friday prayer with the intention of benefiting from a better preacher and an impactful sermon. Sheikh Ibn Baz was asked about moving between mosques in search of a good voice, and he replied that he saw no harm in it, especially if it increases humility and tranquility. As for the hadith (definition): "Let one of you pray in his mosque, and not seek out other mosques," it is weak through several chains of transmission. Even if it were authentic, the prohibition would refer to moving around in a way that leads to disunity among Muslims and causes discord, or it might mean that someone who missed congregational prayer in his mosque should not bother seeking out other mosques.