Thank you both, @Raspiaudio and @Mato. I found the NVS editor (I had previously overlooked the setting on the credit page), have enabled the rotary encoder’s click and played around with the device a bit more.
I’m also looking forward to the video on setting it up with squeezelite although, to be honest, I would prefer some written documentation. Videos are a nice introduction, but they are a terrible format for quickly looking things up afterwards. Guess I’m a bit old fashioned that way - or maybe just plain old. 
Here’s some more thoughts and questions on the device:
- The device is beautiful and very well built. I was a bit unsure when ordering it as it is listed as “wood color” and I feared some cheesy plasticky fake wood surface. The front is also very nice looking and both dials turn smoothly. The knobs and buttons feel solid.
- Sound quality is a bit of a mixed bag. Overall it’s quite good, but the noise / static level is a bit higher than I would have hoped or anticipated. I’ll find out how much an annoyance that is for my intended use case (bathroom radio) in the long term, could well be one of the things one notices when the device is new but forgets in the long run. Time will tell.
- @Raspiaudio, you mentioned that the display blanking is something that can be set in NVS. I didn’t find the corresponding setting, how would I change that? And is it possible to have it behave differently when it’s plugged in vs. when it’s running on battery?
- I understand that the buttons can currently not be used in squeezelite. That is a bit of a disappointment and I think something that should be mentioned on the store page. Out of curiosity, what was the reason to implement them with ADC/resistors? Were there not enough GPIOs?
- Even with the rotary click enabled, I didn’t have much luck actually controlling the device with it. E.g. I can navigate to favorites but haven’t found a way to actually select something to play. Also, I didn’t find any way to go back or left. Is there any guide on how to use the encoder to navigate?
- I got the supplied remote to work but haven’t quite understood the button layout. Any documentation about that? Specifically, is there any button that acts as play/pause? I would have expected “OK” to fulfill that function but that jumps back to the beginning of the current track.
- The charging LED is quite bright, so much so that it’s actually visible through the front panel. Is there any way to turn that off?
- As mentioned before in the forum, the cutout for the screen hides ~1.5mm on each side. It would be nice if there was a setting that squeezelite only used the visible portion of the display.
- Most of the options in the “Now Playing Information” section of the LMS player settings did nothing for me. I only could get some VU and the spectrum analyzer to work. Is there any way to display Elapsed or remaining time or a progress bar?
That’s a lot of text now and I’m very much looking forward to answers, reactions and other peoples’ thoughts on the device. As for spreading the word, I’ll definitely do that but will probably wait a little until I know better how the device handles in actual use. Thanks to everybody who read this far and to @Raspiaudio for developing and supplying the Muse Radio!