I'm a bit confused about your question and what exactly you're trying to achieve but I'll take a shot. The zen stream is a source so it doesn't handle input, it is an input. I'm gonna take a jump here and assume, since you mention all these, that you're looking for a way to use zen stream as a source for both headphone and stereo and still able to watch your DVD concerts from PS5 which is connected to TV and then TV I assume is connected to your stereo currently.
Also unclear what exactly that devialet device is you're streaming to via devialet air protocol, a lot will depend on what inputs that device has. I assume it should have at least an analog input and maybe a digital input so here is my 2 cents:
The easiest setup is to put the zen stream as a source for the Spring 3, then from the spring 3 to your headphone amp via balanced output and also to devialet device via SE output. The Spring 3 outputs to both when playing. You could leave the TV connected to the devialet device but also possible to send signal to Spring 3 via spdif to send all sound through the Spring 3 (which is maybe what you want with a +3k DAC), that way you could also listen you're dvd's on headphone while watching them on the TV.
In terms of control you only need to control the streamer and maybe the input on the DAC if you have multiple sources connected to it. For Deezer, I'm not sure you want to go the zen stream route. If you're using roon its ok (but not deezer support so guess not). If you're on android you might want to wait until chromecast support turns from promise to reality or look elsewhere, if you're an apple user, you can use airplay. Don't bet your money on the native apps, seeing you're gear you want quality components that work well and there still is a lot of DYI feeling to it. Just controlling it from 3rd party apps like Deezer via Airplay/Chromcast is much easier and convenient then.
You could also output directly from zen stream to spring 3 and devialet (if it has digital input) but there are buts... When using the USB output on zen stream (or USB on any streamer probably) the USB output locks and is the only one outputting signal. When using multiple outputs and one of them is USB, switching via UI is required. A bit of a PITA if you ask me. You could output to both devialet and spring 3 via spdif (coax and optical), not sure if switching is required then, probably not.