At first glance, it seems that the intent behind Rashi’s interpretation — “In this parshah, all the weights {of the contributions to the Mishkan...} are enumerated” — is to decipher the word “pekudei” (not as a term denoting appointment, but rather) as a term denoting counting and calculation.
But Rashi himself precludes such an intent by continuing to say, “and there are enumerated all of its vessels...” When “pekudei” means “counting,” the intent is (not “enumeration,” that is, the act of counting but determining) the total count, the specific total value. This is evident from the verse at the beginning of parshas Ki Sisa: “When you count the heads of the Children of Israel םֶהיֵדֻקְפִל {according to their countings}.” Rashi comments, “When you wish to know the sum of their numbers, to know how many they are.” However, this meaning of “pekudei” cannot apply to the clause “all of its vessels for all the work in the Mishkan” because the Torah does not record the number and total of the vessels. Instead, the Torah merely enumerates (“enumerates”) and describes the vessels.
And since Rashi maintains that the expression, “These are the pekudei,” relates to both “enumerations” — the enumeration of the offerings to the Mishkan and the enumeration of the vessels — Rashi clarifies that (a) pekudei” here means appointment and assignment. Rashi also clarifies that (b) just like the enumeration of “all of its vessels for all the work in the Mishkan,” when the verse enumerates “all the weights of the contributions to the Mishkan,” it does not mean that Moshe provided the Jewish people a sum of the total value of the offerings (and how they were used) — to prevent any suspicions, or the like. Instead, he merely enumerates and continues — he itemizes “all the weights of the contributions to the Mishkan” (similar to the enumeration of “all of its vessels for all the work in the Mishkan”).
[For this reason, Rashi carefully chooses his wording, “all the weights of the contributions to the Mishkan are enumerated” (and does not use the term “total” or something similar). By doing so, Rashi intends to clarify again that the verse here does not refer to transmitting the overall “sum of their numbers” (“their sums”). Instead, the Torah only spells out the weights of the donations, “of the silver, the gold, and the copper.”]
The purpose of the enumeration is similar to the purpose of enumerating the vessels for all of the work — that is, both “enumerations” are related to “pekudei” — the role of the appointee:
The enumeration of the vessels is related to the fact that the Jewish people brought the Mishkan and all its vessels to Moshe so that he determined that they were correctly made, etc. (As the verse concludes there, “Moshe saw all the work, and behold, they had done it as Hashem had commanded.”) Therefore, Torah provides a detailed list of all the vessels, as is standard practice — an appointee must ensure that the number of vessels suffice and are fully functional.
The same applies to the counting of the donations to the Mishkan: Moshe, being the appointee and responsible for the Mishkan, kept records of the weights of the donations to the Mishkan.”