Fight can be of different modalities, here the example:
Modality 1.: I am a king of a tiny kingdom of Colchis, a clientele kingdom of the great Roman Empire and I fight against Persian army; but of course I cannot directly confront them, I do not have even weapons to oppose the Persian soldiers, but what I can do is to dig ditches and pile up stones to create obstacles for the Persian army so that my protector Roman army and Roman soldiers may more conveniently defeat the Persians. Thus, Persians are eventually defeated and expelled from Colchis, while I haven't even taken a sword against them, haven't even directly encountered them, but my fight was just to take shovels and spades to create obstacles, while the Roman soldiers did their did.
Modality 2.: Persians attacked Colchis, and the Colchian king gathered his nation and gave them order to fight the Persians to the last drop of blood and through incredible valor and military skills, with a direct encounter with Persians the Colchians managed to defeat them, albeit suffering major losses themselves.
Now, in which modality did Michael and other Angels fight against Satan? The first modality, of course, for the angels do not have authority over other angels, but can only invoke God against them if they stray from Him. That's why in Jude's letter we see the modality of how Michael fights Persia...sorry Satan: he invokes Roman... sorry God to repel him. The same was evidently his fight against Satan also in Revelation, but the modality of fight is not specified there, it simply says that there was a fight.
Christ sovereignly, without prayers to God, ordering cure-providing angels (Matthew 8:13), or demons (Matthew 8:32), as well as the powers of nature (Mark 4:39) to obey Him shows that He Himself is above all angels, above all creation, and therefore God, sharing the same authority with the Father God.
Moreover, Christ invests humans also with the authority that is above the angelic authority, for angels, neither Archangel Michael or Raphael etc., can expel demons by directly ordering them, whereas Paul can do it himself in Christ's name, for he has been invested from Christ with a greater, a supra-angelic, a divine authority (Acts 16:18). Paul (and all the Christians) is king, co-king with Christ, while the Archangel Michael just a servant of Christ-the-King and of his co-kings - us, Christians.