Ostensibly, we can resolve this contradiction in Rashi based on Rashi’s words at the end of his comments on the clause, “These are the pekudei” — (“{In this parshah} all the weights of the contributions to the Mishkan are enumerated...) and all of its vessels for all the work in the Mishkan are enumerated.” In other words, “the pekudei of the Mishkan” does not refer only to the calculations of the donations to the Mishkan but also to the enumeration of “all of its vessels for all the work in the Mishkan” (listed later in the parshah [after the account of the garments of the kohanim] in the passage beginning, “They brought the Mishkan to Moshe.”)
On this basis, we can appreciate the connection between “the pekudei of the Mishkan” and “the work of the Levites” in the continuation of the verse: This matter of “the pekudei of the Mishkan” (the enumeration of the vessels for all its work) is related to the work of the Levites, “to carry, tear down, and to erect.” As the verse says in parshas Naso, “You shall designate by name the vessels charged to them for their burden” (and as understood simply, the appointment over carrying the Mishkan includes the tasks of keeping an inventory of all the Mishkan’s vessels and ensuring that they are kept in working order, etc.).
However, we still need to clarify: Why does Rashi need to say that “the pekudei of the Mishkan” includes the two types of enumeration and that the intent of these words is (not only the calculation of the donations to the Mishkan but also) the enumeration of “all of its vessels for all the work in the Mishkan”? (Doing so is what requires Rashi to interpret that “the work of the Levites” concerns their appointment over the vessels of the Mishkan “to carry, to tear down, to erect....”)
Moreover, at first glance, this explanation is strained: The Torah separates the two enumerations with the account of the Kohanim garments. Thus, it is difficult to say that “These are the pekudei of the Mishkan” (also) refers to something appearing two sections later.
Since Rashi explains the term “pekudei” as denoting enumeration, he should have explained the verse like the (aforementioned) commentators, that “the work of the Levites in the hand of Isamar” means that Moshe transmitted the responsibility of counting the donations to the Mishkan to the Levites under the direction of Isamar.
