Old Arabian speaks “majus” because they lack a hard G sound, similar to Japanese lacking L sound
This isn't quite right. We start with Old Persian (not Arabic) maguš, pronounced like mag-ush. That gets loaned into Ancient Greek as μάγος (mágos), originally referring to Zoroastrian priests and then generally to magicians, sorcerers, and tricksters in general. This gets carried over to Latin as magus (still pronounced with a 'hard' g). The plural of this form is magi, pronounced in Antiquity as mag-ee. As we enter into the Middle Ages, some sound changes happen and most Latin pronunciations soften the G, producing something like maj-ee. At some point in Middle English, the Latin -i plural ending gets replaced with the native English -es plural, producing mages . The singular mage is then derived from that. There's also undoubtedly an influence from French, where an -age ending would always be pronounced with a soft G (ie, the word age).
Looking a bit deeper, the Bible plays a big role here, as the plural of the Greek word, μάγοι (magoi) is used in the original text of Matthew 2:1. That gets translated in the Latin Vulgate as magi, and then I'd presume a Middle English gospel translation as 'mages'. The singular 'mage' then gets derived from that.