the official response from the White House is: Biden called Xi to setup guardrails to prevent open conflict. Biden didn't call for the improvement of the relationship, and he didn't ask for any favor. The reason he called Xi was the US was frustrated at lower level engagement. Xi's stand is confrontation is not good for anyone.
You are wrong. US objective towards China is containment.
This objective trumps any other priority such as climate change (see the sanctions on solar panels made in Xinjiang).
So if the US has publically came out and said that containing China is more important than climate change, then why should Xi believe the US that it totally wants to sincerely cooperate on climate change? Bs.
And lastly Xi' stance is very good. The US as the established Hegemon with deep foundations would love it if it could fence areas where it can defend itself from a rising superpower ("setting up guardrails"). China is now trying to find every weakness in the US and then ruthlessly press on it in order to have space to rise.
This is a 85-15 out of 100, power benefit to the US. So for China to gain ground it needs to reduce that 85 benefit that US holds by any means. In fact, this is an almost zero sum game, wherever China gains, the US loses.
However China is also pursuing unorthodox strategies in order to grow the pie and able to get influence more easily by engaging the developing world in Africa and middle east.
This is a very complex game which why Zhao and Wang Yi were totally correct that climate change cooperation is indispensable from the overall US-China relations.
Lastly, before anyone starts saying how China is ready to burn the world bla bla. China already has its own climate plan which is following. Meanwhile the US has still not made any kind of legislation, only some "Executive Orders" by Biden, which will get cancelled when the next (Trump) President comes in.
If the West wants China to accelerate its already challenging climate plan from 2060 net zero, to 2050, then the West should start giving China at least $200B per year