Aside from the many connections to Moses’ and Israel’s story, the temptation account definitely has a message about Yeshua’s identity. Is it what people think? R.T. France in the New International Commentary on the New Testament series is most helpful.

Some have argued that the temptation centers around Yeshua’s messianic mission:
…(1) if Yeshua could make bread he could get followers
…(2) if he survived a fall from the Temple, this sign would get followers
…(3) if he accepted Satan’s offer of transfer of kingship now, Yeshua could reign as Messiah early.

France says no, that is not it.

It is about Yeshua’s relationship to the Father and the tempter trying to drive a wedge between them:
…(1) Will Yeshua exploit his role as the Son of God? Will he put an early end to the time of testing by making bread from stones?
…(2) Will he require the Father to save him from a fall, pridefully asserting his right as the Son?
…(3) Will he skip the hard road to kingdom decreed by the Father and take a transfer of kingship directly from Satan?

As France observes, Yeshua will face similar temptations as the time of the cross draws near and while he is on the cross.

The list of parallels is not only interesting, but a great clue to the meaning of the temptation story itself.

The note that Yeshua was led up into the wilderness is more than a hint of God leading Israel into the wilderness. Forty days and nights without food, while more similar to Moses’ stay on Mt. Sinai (Deut 9:9), also calls to mind the forty years Israel was in the wilderness. See Jer 2:6; Ezek 20:10; and Amos 2:10 for verses about God leading Israel into and through the wilderness.

Israel was tempted (and tested God) with regard to three things:
…(1) Hunger (Exod 16:2-8), the Manna story.
…(2) Putting God to the test due to lack of water (Exod 17:17:1-3; Deut 6:16).
…(3) Idolatry (Exod 32), the Golden Calf story.

Compare Matthew 4:8 and Deuteronomy 34:1-3, where God showed Moses all of the land.

Yeshua quotes three verses from Moses:
…(1) Deuteronomy 8:3, in order to teach you that man does not live on bread alone, but that man may live on anything that the Lord decrees.
…(2) Deuteronomy 6:16,  Do not try the Lord your God, as you did at Massah.
…(3) Deuteronomy 6:13, Revere only the Lord your God and worship Him alone, and swear only by His name.