No expertise of any kind but I personally don't think they would, depends on the situation.

With Covid I think it depends on your work/life situation. I had a shitload of anxiety about it early on, nearly quit my job, eventually kind of realized it kind of is what it is if I get it I get it and if I die I die. If I had been allowed to work from home I have no doubt my anxiety about the situation would be much worse and things like grocery trips would still seem like a thing. Kind of a gotta be thrown in the water to learn to swim type of deal. Not trying to judge but you hear the lifestyle some of the people on the covid sub are bragging about and I feel like they might need therapy. If anything maybe they'd handle lockdowns and restrictions better but that seems like it'd be more anger than stress.

Climate change collapse I'd doubt it even more. Maybe people with anxiety have more supplies but I'd guess they have less survival skills and are far less ready to suddenly have to abandon their home/apartment for flooding/fire evacuations. Maybe I'm just looking at myself too much but I feel like something in the realm of agoraphobia and having control of your surroundings/situation is pretty common for anxiety sufferers.