Space technology is a very vague term.
It depends on whether you're talking about communications satellites and other types of commercial satellites, or (in contrast) scientific instruments such as space telescopes and unmanned exploratory vehicles.
I imagine that the former (the commercial satellites) are primarily handled by industry, and it would seem to me that engineers would be the ones designing and building them.
That having been said, there is a HUGE role for engineering/applied optics in astronomy nowadays. With any scientific space mission, the the overall design and specific design parameters of the spacecraft carrying the suite of instruments is dictated by the science that that spacecraft or orbiting observatory is supposed to carry out. The criteria are often collectively referred to as the science goals or science drivers behind the project. In other words, you cannot design it without having some idea of its intended purpose and what it must be capable of when it is up there in terms of its resolution, wavelength sensitivity, detector type, and data storage and readout requirments.
The point I'm getting at is that it's the astronomers in the first place who dream up these fancy new telescopes and other instruments, and come up with the initial purpose, concept and design, and funding proposals. Astronomers sometimes even get their hands dirty designing and building the hardware and software for that instrumentation. This is especially true of the highly specialized instruments needed to do the science such as spectrometers and polarimeters and specialized detectors. In many cases, these are instruments that nobody has built before. They have been designed with a specific scientific purpose in mind. Whether the astronomers then continue to see things through to the construction and testing phases depends largely on the scale of the project. For example, one of the professors in my department was involved with the Wilkinson Microwave Anisotropy Probe (WMAP). He and his fellow scientists are sort of "experimental" cosmologists. They're used to actually building things that will help answer questions about the universe. That having been said, this was a very LARGE project being run by NASA (who was actually going to be launching it). So at a certain point, all of the various instruments and pieces of the space probe being developed by collaborators at various universities were brought together at NASA and the handful of scientists began working with a whole TEAM of engineers on putting the thing together. He described it as something like 50 people worrying about everything from whether the spacecraft would survive the launch to what its thermal properties were to whether its electronics would behave properly in space and be sufficiently shielded from noise to where the spacecraft was getting its power from etc. These are things that are more peripheral to the scientific aspects of the space probe and are more likely to be the same from one space probe to another. As a result, they can easily be handled by NASA engineers specializing in mechanical vibrations or heat transfer or electronics or power systems or... who have no background in astrophysics.
If it's a small enough project...you might not need external engineering. The MOST satellite, a so-called microsatellite the size of a suitcase was designed and built by a professor within my deparment and his team (he may have had other collaborators at another Canadian university too...but the point is that the project was carried out entirely by astronomers at universities and their students). Then you just have to find somebody to launch it for you. In his case, that was the Canadian Space Agency (CSA) (our counterpart to NASA, I guess). Of course, the CSA doesn't have any launch vehicles or launch facilities, so they in turn asked whoever it is who launches their satellites to launch MOST.
Another example is NASA's JPL (Jet Propulsion Laboratory), which, contrary to the name, seems to be the biggest source of American scientific space missions, including many of the planetary space probes and space telescopes you might have heard of (at least the American ones). Yet, it's in Pasadena California right near the California Institute of Technology, and many astrophysicists from Caltech are the ones who work at JPL and are involved in these scientific space missions.
I read your other thread regarding astrophysicists and their salaries. If you are on the fence regarding whether you want to devote your life to pure science right from your first degree, or whether you'd rather get a degree that some would consider more "pragmatic" such as engineering, then let me give you an example (myself). I was on the fence. I liked physics and astronomy. But I wasn't sure about getting a four-year undergraduate physics degree. Then what? What if it turns out I don't want to be immersed in academia for the rest of my life? So I enrolled in the Engineering Physics program at UBC. I liked the concept of it...the idea that you're getting the background you need to bridge the gap between the latest advances in physics, and technological applications that stem from them. Examples would be nanotechnology, quantum computing, high-temperature superconductivity, semiconductor lasers etc. It's an accredited engineering degree. I know a few universities in Canada offer it. I don't about undergrad programs in the U.S. I should warn you that it's not a walk in the park. It's a LOT of work. For me it essentially amounted to an undegraduate physics degree PLUS an electrical engineering degree (but at the end of it, you only have one degree to show for it...haha!). Now that I'm close to graduating, I've decided that I do indeed want to pursue a graduate degree, most likely in the area of astronomical instrumentation , which is exactly what I have described above. It is the building of highly specialized scientific instruments for astronomical observations. Obviously having engineering skills is a huge help, and gives you an advantage over pure astronomy students who go on to become involved in such projects. But the flip side is that without a knowledge of astronomy and astrophysics, you won't understand the purpose behind these instruments or why they are being developed with certain capabilities. You're solving problems that DON'T already have known solutions...using your knowledge of fundamental principles. This in contrast to conventional engineering, which often involves improving upon or optimizing solutions to already well-understood problems for specific applications. I'm generalizing here. I apologize to all of the many bright engineers working in industry with 30 years of experience and tons of patents who have done pioneering work to advance the frontiers of technology and improve our quality of life. So let me give an example to illustrate what I mean. One example I've come across is the SCUBA-2 detector. It's going to be installed on a ground-based telescope in Hawaii. It's much more complex and unique than the image sensor in your digital camera. That's because it is meant to detect submillimetre wavelength radiation (longer than far infrared, but shorter than microwave or radio). The problem of how to detect this type of radiation in such a way that maximized both sensitivity and resolution hadn't been solved until they developed SCUBA-2, which exploits superconductivity among other things. The solution stems from fundamental physical principles. One of my supervisors was telling me about its design, and how it would be difficult for them to improve upon it. It's about as good as it can be, because the only limitations to its performance now are essentially those that are a result of the laws of physics themselves. He dropped the phrase "the quantum limit" several times during the conversation.
The point is that with my background, I have options. Even after I finish my graduate degree...I don't think I will have slammed any doors shut for myself by focusing on astronomy for that portion of my life. At least, not from examples I've seen and heard about while talking to my professors.
Finally, there are other areas of space techonology that we haven't discussed. I don't think that astronomers are involved AT ALL with rocketry and manned spacecraft . That would seem to me to be the purview of aerospace engineers (not to mention a whole load of other types of engineers). Astronomers work on unmanned scientific missions...for the science. Also, space suits, space habitats, space stations, space propulsion...not really relevant to astronomers. Individually they might be interested in these technologies...but it's not their job. I think that goes without saying.
