...some administration officials see China as a lost cause and prefer to treat China and Russia as committed partners...

I, Benjamin Harris, not an administration official, have some thoughts on this which, owing to age, the press of immediate concerns with Ukraine and mental gear work that at present is too slow to engage on more than one subject, will defer to a subsequent post.
...
...three increasingly authoritarian NATO nations — Poland, Hungary and Turkey — play key roles in the coalition aiding Kyiv.
...
...Russia’s invasion has supercharged the Biden administration’s efforts to restore the morale of a NATO alliance that Mr. Trump undermined.

But the alliance includes three nations — Poland, Hungary and Turkey — whose democratic backsliding has troubled the Biden administration. Hungary and Turkey were pointedly excluded from Mr. Biden’s global democracy summit in December, and the European Union has cut billions of euros of funding to Poland and Hungary for what it sees as erosions of legal and democratic principles. Now all three countries are participating in the coalition against Russia.

“In times of crisis, there is sometimes a tension between our values and our interests,” said Andrea Kendall-Taylor, a senior fellow at the Center for a New American Security. “In the short term, we’re going to have to prioritize pushing back against Russia, at the risk of taking our foot off the gas on the democracy and human rights concerns that had been at the front and center of the Biden administration’s agenda.”

I disagree that Poland and Turkey (I don't know enough about Hungary to ignorantly opine.) present a conflict between our values and interests. Turkey has not joined in sanctions against Russia. Poland is trying to drag NATO and the U.S. into World War III. Democracy, achieved or well-pathed, is one of the key membership criteria for admission to NATO. In Poland and Turkey there is serious backsliding on democracy and they are not in step with NATO. Hungary, I don't know. Poland and Turkey do not any longer meet NATO membership criteria. Can't we kick them out?

Mr. Xi’s persistent support of Mr. Putin, with whom he shares a drive to dilute American power...

It is about power, but it is more than about power. See below from a separate NYT article on China from Feb. 27:

...there is no sign that Xi did anything to ward off the invasion, if he knew it was coming.

Since this article appeared others have. In fact, Xi did have advance knowledge of the war. Putin told him at the Beijing Winter Olympics. Xi asked that he hold off until after the closing ceremony and Putin complied. The war started on Feb. 24.

Xi's senior advisers rebuffed American requests to use China’s influence with Mr. Putin to discourage an attack; instead, China shared the Americans’ intelligence with the Russians and accused the United States of trying to sow discord, according to American officials.

So we share our intel with China in good faith, they already know, and tell the Russians that we know.

...

That relationship seemed to reach a new peak at the Olympics. [Indeed, it did!] After their meeting, the leaders issued a lengthy joint statement that raised alarms in Washington.

It was the first time China had explicitly endorsed Russia’s demand for a halt to NATO expansion...

The two leaders also vowed to resist American-led efforts to promote pluralistic democracy [That is the "more than about power" part] and said they would fight foreign influence under the guise of what both call “color revolutions,” after the popular uprisings in former Soviet republics like Ukraine and Georgia.

-more-