Can fiduciary standards of care, prudence and loyalty be imposed on
Not under existing law, with the possible exception of emoluments (which basically means "kickbacks"), criminal theft of public property, and certain civil rights violations (or for the unofficial private acts of the U.S. President, for example, with regard to a private trust of his family for which he or she is the trustee).
There is not clear precedent one way or the other on the possible emoluments exception even though this issue was litigated in the Trump Administration. Most of those cases were dismissed on procedural grounds or dismissed as moot when he left office.
Could congress pass a law setting a fiduciary standard of care in some
fiscal matters, and enforce it (e.g., through impeachment?)
Congress can impeach for any circumstance that it deems to be a high crime or misdemeanor, and its determination of that point is non-justiciable.
It is not obvious whether this obligation could be imposed by statute consistently with the constitution under existing U.S. Constitutional law.
This would be basically a question of first impression, or at most, a question for which the precedents available are so stale that the continued applicability of these precedents in the light of new legal developments in constitutional law jurisprudence is uncertain.
There is law that makes fairly clear that such a duty could not be imposed upon the President of the United States acting in his official capacity by state law under the supremacy clause and the general considerations of federalism, however. This is important, among other reasons, because the standing requirements of the federal courts do not apply with full force to state courts applying state law.
One important constitutional issue in this context would be who has standing to enforce such a duty, since standing is a matter of the subject-matter jurisdiction of the federal courts.
Current standing jurisprudence does not allow for "citizen standing" or "taxpayer standing" nor does it usually allow individual members of the U.S. House or U.S. Senate to have standing, nor does it usually allow one part of the Executive branch to sue another part of the Executive branch of the United States government. In most cases, this means that if the President's actions cause only generalized fiscal harm to the United States as a whole, that no individual could have standing.
One exception might be for a qui tam action in which an individual is deputized to act as a prosecutor for the United States government itself (with the relief obtained payable to the United States) in a civil action in exchange for a statutorily determined contingent fee related to the amount recovered. I'm not familiar with the constitutional dimensions of standing in such cases, which is mostly obscure at the outer limits because the existing statutes that authorize this have been upheld on a piecemeal basis with other their particular procedural details (including a right of the Justice Department to take over such lawsuits against private parties) and the fact that these suits are usually limited to suits against people other than government officials. It is closely related to the largely open question of whether, contrary to Justice Department policy, it is constitutional to bring federal criminal charges against a sitting President. These issues are closely related to the Unitary Executive theory of constitutional law which the current U.S. Supreme Court has been inclined to follow (which disfavors allowing liability for the President, at least, while in office).