Matthew 10 is a record of what is commonly called “the Limited Commission.” It is so called because, as opposed to the Great Commission of Matthew 28 and Mark 16 which included the whole world, this sending was only to the house of Israel (vv 5-6).
As with any delegated authority, there must be some means of proving that authority. In the days of the Old Testament, one could provide documentation sealed (authorized) with the king’s signet (Est 3:12; Dan 6:8-9, 17).
In this case, as with many others in both Testaments, God’s authorized delegates were given miraculous powers to prove the source and authority behind their message. Such was done for Moses (Ex 3-4), Elijah (1 Kgs 18), and the unnamed man of God (1 Kgs 13). In like fashion, miraculous powers were given to the 12 as proof of their divine commission (vv 7-8).
Additionally, consider that Divine commission, approval, and miraculous power were no protection against verbal abuse or physical persecution. Jesus warned the 12 that they would be placed on trial and physically abused (vv 16-18). But the apostles were again given provision in these cases. Rather than be worried about getting caught in contrived arguments or questioning, the apostles were promised divine and irrefutable testimony in the face of their accusers as well as in the presence of the Gentile (Roman) courts (vv 19-20), “for it is not you who speak, but the Spirit of your Father who speaks in you.”
One of the first real tests of this promise was manifested in the life of Stephen in Acts 6:8-10, wherein it is said that those who disputed with Stephen “were not able to resist the wisdom and the Spirit by which he spoke.”
Afterward, having been dragged into court, Stephen again gave a marvelous recitation of Jewish history. I believe this sermon was intended to lead the hearers to Jesus. Unfortunately for them, they proved themselves unworthy of this great message by putting Stephen to death. But Stephen was prepared (Acts 7:55-60)!