@ansx
Whichever DAC/headphone amp you end up choosing, and given your particular requirements, I think that you'd benefit from powered monitors, as opposed to passive speakers. With powered monitors you eliminate the need for your DAC/headphone amp to do extra duty as a speaker amp. This means that all you really need is a DAC/headphone amp with line-level RCA outputs and not a headphone/output switch. The use of powered monitors also means that you can use any DAC/headphone amp with RCA outputs, even if those outputs are controlled by the volume knob (though that would possibly mean that you'd need to unplug your headphones when using the RCA outputs. But that's not the end of the world).
You mentioned that you found a Sony soundbar that you believe will suit your needs. And maybe it will, given all of your considerations. However I would like to make an alternative suggestion: I suggest that you consider a pair of Edifier powered speakers.
Edifier makes a range of powered bookshelf speakers, ranging from under $100 to nearly $1100. Given the price of the Sony soundbar (at $250), I highly - and I do mean HIGHLY - recommend that you consider the
Edifier R2000DB speakers. In fact, I feel so strongly about this recommendation that, despite lurking on this site for several months, I created an account solely for the purpose of recommending these speakers to you.
I own three pairs of Edifiers, including the R2000DBs, which I use as my computer speakers in my home office, and I can tell you that they sound outstanding (especially for the price), and that they are very well built.
Here is a YouTube review of the (more expensive, at $400/pair) Edifier S2000Pro speakers. I included a link to a review of those speakers, despite them being beyond your current budget, because it is a comprehensive review that will give you a good idea of the care that Edifier puts into building their speakers. (
Here is a much more amateurish, less comprehensive review of the R2000DB speakers.)
Of course, these are bookshelf speakers, which means that they will take up more space than the Sony soundbar that you are considering. However the speakers will be off to the side and not right in front of you, on the desk (mine are actually 50" apart and angled slightly in, since they are acting as near-field monitors). But if you have some room off to the side of your monitor (and pushed all the way back on the desk, of course) then powered monitors (and not a crappy soundbar) are something that you should strongly consider.
As to your original question: a output switch shouldn't be necessary when using powered monitors. So look for any DAC/headphone amp that's capable of driving your headphones and that has a pair of RCA outputs.
Good luck!