Just because Tesla is worse than others doesn’t make it not self-driving.

The fact that Tesla requires a human driver to take over constantly makes it not self-driving.

so they can take over instantly.

Humans fundamentally can’t do that. If you sit a human in a self driving car doing nothing for hours, they won’t be able to react in a split section when it is needed.

The Human isn't supposed to be "doing nothing". The human is supposed to be driving the car. Autopilot is simply keeping the car in the correct lane for you, and also adjusting the speed to match the car ahead.

Tesla's system won't even stop at an intersection if you need to give way (for example, a stop sign. Or a red traffic light). There's plenty of stuff the human needs to be doing other than turning the steering wheel. If there is a vehicle stopped in the middle of the road Tesla's system will drive straight into it at full speed without even touching the brakes. That's not something that "might happen" it's something that will happen, and has happened, any time a stationary vehicle is parked on the road. It can detect the car ahead of you slowing down. It cannot detect a stopped vehicle.

They've promised to ship a more capable system "soon" for over a decade. I don't see any evidence that it's actually close to shipping though. The autonomous systems by other manufacturers are significantly more advanced. They shouldn't be compared to Tesla at all.

Is anybody actively testing them in bad weather conditions?

Yes. Tens of millions of testing and they pay especially close attention to any situations where the sensors could potentially fail. Waymo says their biggest challenge is mud (splashed up from other cars) covering the sensors. But the cars are able to detect this, and the mud can be wiped off. it's a solvable problem.

Unlike Tesla, most of the other manufacturers consider this a research project and are focusing all of their efforts on making the technology better/safer/etc. They're not making empty promises and they're being cautious.

On top of the millions of miles of actual testing, they also record all the sensor data for those miles and use it to run updated versions of the algorithm in exactly the same scenario. So the millions of miles have, in fact, been driven thousands and thousands of times over for each iteration of their software.