A covenant embodies and expresses a commitment. Goldingay seems to me right to suggest that the metonomy here is little different from others such as being turned "a light to the nations" or Abraham being "a blessing".
"In each case the idea is that the person not only mediates but also embodies the thing, as Jesus will be resurrection and life rather than merely bringing it. Genesis 12:1-3 suggests that Abraham will be the embodiment of Yhwh's blessing, demonstrating in a life what it means to experience that blessing, and arousing in other people a desire for it. As a covenant with people the addressee here will embody and express Yhwh's commitment to people."
John Goldingay, The Message of Isaiah 40-55 (T & T Clark, 2005), 164.And, given that Israel is called to be the servant, "people" likely refers to God's commitment to humanity, as in the parallel "a light to the nations."
