Range anxiety is the same -- most of the time, people drive between home and work. For most people, this fits in the range for an electric. If you really want to drive across the country, you can just rent a car, and this will be much cheaper than owning an ICE for how often you'll actually need to do it. If you're lucky enough to have the space and money, and need two cars in the first place, then it makes sense for one to be electric: the one driven most often, and then the ICE vehicle for when electric is not appropriate.
Also, if I'm driving with what I call the "idiot light" (low fuel) on, then I'd best go fill the tank. When that warning appears if I have less than 50 km of range I'd be surprised. A low range BEV would feel to me like always having that light on.
In many European countries, that would be a border-to-border trip.
But as the saying goes: Europeans think 100 miles is a long trip and Americans think that 100 years is old =)
It's not. People are somehow really dreading having to (predictably) stop for a 45 minute charging stop in the rare case they actually do have their trip exceed the maximum range (again, unlikely if you leave on a full charge and don't plan to leave the country).
It will tell you when you step into the car what your range is and you can plan right then and there where to stop for lunch/coffee. Most EV drivers do exactly that. Problem solved.
ICE car drivers don't do that and typically just have unreliable data instead. You might have 70 km of range or 20. Hard to tell when the needle is close to 0. You might be going up hill or downhill and that might affect what the needle says. It doesn't even indicate range, just fuel volume.
So, premature/redundant fuel stops are probably more common than running out of fuel, or indeed battery. By the time you run out of battery, your car will have been drawing your attention to that for quite some time. So, you'd be right to feel anxious about that happening to you because you'd end up looking like the fool you are.
Most drivers take the annoying planned charging stop over that some tens of miles before they'd run out. It's more a case of range annoyance than anxiety. In the end everything has a price and if you can afford to fill up your gas guzzling SUV to burn way more fuel than you'd strictly need to get from A to B, that probably has more to do with other forms of anxiety than with the actual range of the car.