Deeper understanding as to why Isaiah 49:3's reference to "My Servant, Israel" fits in the larger context of Isaiah 49's Messianic prophetic account

Let us first point out that although the Servant in verse 3 is called Israel, it is still singular. Just like two previous verses, it talks about one specific individual.

The second fact to consider is that Isaiah's book is heavily influenced by the Song of Moses (Deuteronomy 32). That is the first place where the idea of God's servants appear. If you read closely you will be able to identify two groups within the ethnic Israel. The obedient ones called servants. And the disobedient majority called:

• corrupt and not his children; to their shame they are a warped and crooked generation. (32:5)
• foolish and unwise people (32:6)
• nation without sense (32:28)
• vine of Sodom and of Gomorrah; grapes that are filled with poison, and clusters with bitterness (32:32)

The same idea of two groups of peoples within the ethnic nation of Israel is expressed in Malachi 3&4.

The third thing to consider is the purpose of the nation of Israel. After the confusion of languages of Genesis 11 humanity was split into 70 nations. If you count all the names in Genesis 10 you will end up with 70. In the next chapter after the tower of Babel, the focus of the book shifts to Abram, Sarai and their descendants. God disinherited the nations and created a new one from an old couple as a rescue plan for the humanity. That new tribe was created to be the nation of priest, interceding for the other 70. That is why the whole family of Jacob was numbered 70 when they moved down to Egypt (Genesis 46:27). Unfortunately, the potential that the nation of Israel had was wasted because of the golden calf event. Instead of becoming the nation of priest, they became a nation with priest themselves.

Keep also in mind that the blessings given to Abram/Abraham (Genesis 12 &22) and David (2 Samuel 7) were going to be funnelled through an individual.

Isaiah puts all those ideas into the blender. He prophesied about an individual born out of the ethnic nation of Israel that was going to reshape the idea of the people of God and recentre it around himself. The physical Israel was a picture and foreshadow of the spiritual Israel, called by Paul the Israel of God (Galatians 6:16). All the spiritual ideas revealed in the NT had their physical pictures in the OT. Things like the true temple of God, the sacrifices, the priesthood, etc. Israel is just the same way. That is why Paul always calls the unbelieving Jews, Israel according to the flesh. And at the same time he calls the believing gentiles the real Jews (Romans 2:28; Philippians 3:3). An Israelite is a person chosen by God, that believes in the ultimate Israelite, the Messiah, regardless if he/she is a Jew or a gentile. For the same reason, the twelve chosen by Jesus did not physically represent all the twelve tribes. Jesus did a new thing based on the old. In the same fashion, he picked up where the physical Israel failed and sent the new 70 to the nations (Luke 10).

In conclusion, both of your interpretations are correct. Jesus is the embodiment of the nation of Israel and an example to follow. Matthew 2:15 is the best proof of that when in typically midrashic fashion he describes the return of Jesus from Egypt as the fulfilment of Hosea 11:1.

Albert Barnes addresses this question in some detail, which I will quote only in part:

The only other interpretation, therefore, is that which refers it to the Messiah. This, which has been the common exposition of commentators, most manifestly agrees with the verses which follow, and with the account which occurs in the New Testament.

The account in Isaiah 49:4-8, is such as can be applied to no other one than he, and is as accurate and beautiful a description of him as if it had been made by one who had witnessed his labors, and heard from him the statement of his own plans. But still, a material question arises, why is this name 'Israel' applied to the Messiah? It is applied to him nowhere else, and it is certainly remarkable that a name should be applied to an individual which is usually applied to an entire people. To this question the following answers, which are, indeed, little more than conjectures, may be returned:

1. Lowth and Vitringa suppose that it is because the name, in its full import and signification, can be given only to him; and that there is a reference here to the fact recorded in Genesis 32:28, where Jacob is said to have wrestled with God, and prevailed, and was, in consequence of that, called Israel. The full import of that name, says Lowth, pertains only to the Messiah, 'who contended powerfully with God in behalf of mankind.'

2. It is common in the Scriptures to use the names which occurred in the history of the Jews as descriptive of things which were to occur under the times of the Messiah, or as representing in general events that might occur at any time. Thus the names, Moab, Edom, Ashur, were used to denote the foes of God in general; the name of Elijah was given to John the Baptist (Hengstenberg).

3. In accordance with this, the name David is not unfrequently given to the Messiah, and he is spoken of under this name, as he was to be his descendant and successor.

4. For the same reason, the name Israel may be given to him - nor as the name of the Jewish people - but the name of the illustrious ancestor of the Jewish race, because he would possess his spirit, and would, like him, wrestle with God. He was to be a prince having power with God (compare Genesis 32:28), and would prevail. In many respects there would be a resemblance between him and this pious and illustrious ancestor of the Jewish people.

In whom I will be glorified - This means that the result of the Redeemer's work would be such as eminently to honor God. He would be glorified by the gift of such a Saviour; by his instructions, his example, the effect of his ministry while on earth, and by his death. The effect of the work of the Messiah as adapted to glorify God, is often referred to in the New Testament (see John 12:28; John 13:31-32; John 14:13; John 16:14; John 17:1-5).

That is, "Israel" is a name applied, with some considerable justification, to Messiah as well - taking "Israel" as a shadow of the true Messiah.

The Pulpit commentary reaches the same conclusion:

Verse 3. - Thou art my Servant, O Israel. That the literal "Israel," is not intended appears plainly from ver. 5. The Servant himself is addressed as "Israel," because he "would stand as a new federal head to the nation" (Kay), which would be summed up in him, and also because he would be, in a truer sense than any other, an "Israel," or "Prince with God." In whom I will be glorified (comp. John 13:31, "Now is the Son of man glorified, and God is glorified in him"). He who is "the Brightness of the Father's glory" sets forth that glory before men, and causes them to glorify him, both with their tongues and in their lives. Isaiah 49:3