WASHINGTON — Brett M. Kavanaugh is now an associate justice of the Supreme Court, leaving the exhausted Senate to contend with the smoldering aftermath of his vitriolic confirmation fight, one that members of both parties worry did lasting institutional damage.

Accusations of unethical conduct. Personal attacks. Threats of new investigations into leaks. Vows of future retribution. Suggestions of bad faith. And hanging over the conflict was the Republican decision in 2016 to block President Barack Obama’s nominee to a Supreme Court vacancy that occurred 11 months before the end of his tenure.

“It has not been good for the Senate, none of this,” said Senator Richard C. Shelby, Republican of Alabama, who has been a member of the chamber for more than three decades. “Too much estrangement on both sides. We in the Senate have to understand that we have differences. It shouldn’t be personal.”

Confirmation fights tend to bring out the worst in the Senate, given both parties’ intense focus on the courts as they play an ever-greater role in sorting out legislative and societal disputes. But the institution has been struggling for years with a rise in polarization and partisanship, leading to decisions by both parties to try to break the gridlock by essentially forcing through rules changes on nominations.