For example, smoking probably causes more deaths than Covid. So, while it may be perfectly true that things like smoking and pollution are bigger public health issues than Covid, we never spoke of a "smoking crisis", and justifiably so.
The thing that makes a crisis into a crisis is that it's highly discrete in time and there is a temporally very limited window of opportunity to take action. This is true of Covid, but it's not true of smoking or pollution.
A politican speaking of a climate "crisis" is engaging in the same psychological manipulation tactic as a radio commercial telling you to "act now on this limited-time offer", or a used-car salesman telling you that you have to buy that car right now, because this other guy definitely just called and is now on his way to the lot, and will likely buy the car you're interested in as soon as you leave the lot.
Things like permafrost melting and releasing more methane?
That is your definition, but not necessarily the one meant by others. From Merriam-Webster (https://www.merriam-webster.com/dictionary/crisis):
"Essential Meaning of crisis : a difficult or dangerous situation that needs serious attention"
[...] Definition 3b: "a situation that has reached a critical phase // the environmental crisis"
Besides: The definition is a really bad one, as it's circular.
If we can kill all the disease causing mosquitoes as well, then we will remove another huge cause of human disease.
What are you referring to?
(The west has also collapsed bird populations in the service of agriculture, just over a longer period and combined with crashing the insect population as well)