College courses often start teaching applications of physics, applications of math and applications with already invented circuits. We call this engineering, with the main goal of understanding and applying circuits. However many engineers will use standard building blocks, like the standard opamps circuits and off the shelf DC/DCs, and then call it a day.
A masters can go into more in depth theories or generalizations, with more comprehensive evaluations of circuits. Students will learn to read and derive new models and apply them. An average master thesis will include a literature study of state of the art research and then doing something with it. That can range from applying it or taking a stab at extending or doing something different. For many students this can be a bit of a trial to see if perhaps a PhD will fit them.. A lot of master student projects can eventually be published by either a supervisor or the student itself.
If a student likes doing research, writing it properly and making sure it collaborates within the community of research (instead of just being a tone-deaf plea), then go ahead and start a PhD.
There are plenty of topics to do a PhD in EE. Circuit design is a prime example, especially for chip design. Electrification of all industries is still not complete, so power electronics is still necessary. We also need build better amplifiers, RF mixers, frequency synthesizers and receivers for next generation modems. 5G or 6G doesn't come falling from the sky for free, and it's a collaboration between industry and academia to derive a new standard. Same goes with better ADCs, DACs, PLLs, etc. And antenna's are also designed by EEs, with lots of new stuff tried as well (new frequencies, shapes, arrays, multi-modes, etc.).
We need people to design PDKs for every new CMOS process node. EE can span well into computer engineering and embedded systems in order to understand what those sectors need to succeed well. Likewise, there is a lot of applications in signal processing, where linear system theory, probability theory and electronics is necessary to work on new DSP algorithms. This can span from a highly specialized algorithm only used by 1 application to something that is possibly generalized like approximate computing. Most research projects however do need a vehicle of research, so sometimes applications are a bit of a side effect to what the research is really about.
There is also lots of research on mixed signal designs (like partial analog, partial digital computing), or completely new architectures. System design is a giant topic in itself. Some PhDs will be about designing a single component in a new or better way, whereas other PhDs want to demonstrate novel applications by combining state-of-the-art research and extending upon it.