Yes, when you are recording a video, the camera is occupied, and you can no longer open a higher resolution to save the picture. 1080P is the maximum resolution for hardware encoding. If you’re trying to record video at a higher resolution, but software encoding is required, you can save the resolution you want.
I have understood that a recording of a 1080p video doesn’t use the full sensor area (and shrinks it down), but just a portion of it.
So my solution / workaround is to keep using 1080p (to benefit from the hardware accel.), but set the camera mode to 2160p. That drastically improves image quality, but limits the FPS to 18, down from my previous 30. To compensate for the introduced motion blur by the lower frame rate, I increase the shutter speed by a lot and compensate for the loss in brightness by slightly adjusting brightness, contrast and EV parameters.
This results in a crisp and detailed 1080p video feed that contains all the details I need, so I can easily grab stills from the output of this feed.