The people who claim "only X years left to save the world from severe climate change" are stretching the truth for effect or don't understand the primary research well enough. There are certain milestones that we'll pass if we don't make deep emissions cuts in those X years, but there's not a bright dividing line between "ok" and "doomed." Telling people that there is a bright line coming up in just a few years is likely to induce cynicism/apathy when we start living on the far side of that line.
Overall it turns out there is a modest improvement in the U.S. and the other Western industrialized countries.[And even with the modest improvement in the Western industrialized countries, they are still putting massive amount of carbon into the atmosphere every year.]
However there is a worsening in the third world--and they are responsible for more emissions that the Western industrialized countries. Thus for example you see articles like:
Mexico was once a climate leader – now it's betting big on coal
https://www.theguardian.com/world/2021/feb/15/mexico-coal-fo...
That's true for new emissions, but remember that various greenhouse gases once emitted stay around in the atmosphere for a while.
For CO2, a while is 300-1000 years. The US plus Europe emitted about 58% of the CO2 that is currently in the atmosphere.