I’ve presented a few WWDC sessions including two video sessions, though nothing as huge as the keynote or platform state of the union. I can answer most questions you have about the process.
The screens shown in WWDC sessions are usually screen captures from real devices. Development of the slide decks starts with a template deck that has the styles, fonts, and color themes for that year’s sessions. It includes slides that look like the latest devices, with precise rectangles the right size where screen captures will fit. As people develop their sessions they use these slides as placeholders for screenshots, animations and videos.
During development of the OSes the code branches for what will become the first developer seed. Before WWDC, one of the builds of this branch gets marked as ready for final screenshots/videos. The idea is that the UI is close enough to what will ship in the first developer seed that the OS and sessions will match.
Once that build is marked, the presenters take their screenshots and those get incorporated into the slides.
You wrote “It wasn’t just a screen recorder thing”. What makes you say that?
You asked about specialized software. Apple OS engineers have to use what are called “internal variants” of the OSes during development. These have special controls for all sorts of things. One fun thing to look for in WWDC sessions: the status bar almost always has the same details, with the same time, battery level, Wi-Fi signal strength, etc. These are real screenshots, but the people taking the videos used special overrides in the internal variants to force the status bar to show those values rather than the actual values. That makes things consistent. I think it avoids weird things like viewers being distracted by a demo device with a low battery.