Fine.
Democratic Party operatives have raised these purported ethics concerns about GOP-appointed justices in Democratic Party periodicals to fuel Democratic Party Senators in their effort to impose oversight of the Court, ostensibly on ethics grounds. You assert that these claims, plus decisions with which you disagree, have created "instability of the court as an institution."
That, my friend, is a political opinion.
Indeed, later in your piece, you say that "increased scrutiny" is having the intended effect of "leading people to speak up about cases" where a justice's impartiality might reasonably be questioned. Yes, that's the point of the criticism, to create an impression that the impartiality of certain members of the Court might be questioned. Which members might that be?
Your dismissal of various counter-arguments (e.g. Alito's "weakly evidenced dismissal") makes that clear, and after reiterating your support for Senate Democrats to act more aggressively, you turn to Kagan's suggestion that adopting a code would be helpful in persuading others that the Court is adhering to "the highest standards of conduct."
Note that she doesn't say they are doing anything other than that now, just that a formal code would be helpful to address criticism. But you suggest that even if the Court were to adopt a code, it isn't certain that all justices would adhere to it. Which would those be? Well, of course it is those justices that speak with conservative advocacy networks and lawyers that write in the WSJ. They cannot be trusted to adhere to a formally adopted code of ethics for the Court. And that's a problem, you say, because the Court may have to address matters relating to Trump and elections.
"If the justices can't create an environment in which people believe that ethics matter," the Court just might deserve it when people stop adhering to Court decisions. For example, the Court's credibility as relates to Alabama is on the line if the Court doesn't decide in favor of Democrats. Just as it would be if the Court were presented with a case involving Trump and the 2024 elections. Indeed, any solution short of what you advocate means that "questions, and instability, wll fester."
Advocacy is fine, advocate away. But an honest, unbiased treatment of the issue might consider the political motivations of Senate Democrats, the writers and periodicals bringing such issues to the fore, and the proposed solutions you advance. Instead, it seems such motivations are pure, and it's only those ethically challenged GOP-appointed justices and their GOP supporters that are politically motivated.
FWIW, I'm not a Republican, I support a balanced Court and I prefer greater disclosure by the justices. I'd also love to see a mandatory retirement age.
But I am deeply suspicious of the motivations of both political parties and believe the independent judiciary is essential for the preservation of this nation, clearly one of the foundational principles for our system of government. Thus, I disagree with these efforts by one political party to impose political oversight of the Court, regardless of whether it's premised on purported ethics concerns or otherwise. Members of the Court have built a very public career over many years. They've been appointed by the executive branch, survived the confirmation process and associated background investigations, and they've been confirmed by the Senate. I absolutely trust their ethics more than I do political actors like the Senate Judiciary Committee, regardless of the political party of the President appointing them.