Just for clarity as even I get lost especially on Sundays ;-)
Are you looking for a Splitter or Switch ?
An HDMI splitter does one thing: takes one HDMI signal as its input and make multiple copies of it on its outputs. It’s useful if you want to see the same content on multiple screens.
An HDMI switch can be used to do one of two things: take multiple HDMI inputs and allow a single monitor to choose one of them to view, or sends a single input to your choice of multiple monitors
Some switches can act as a splitter also, but are more expensive and not sure if you have considered a way to extract audio from a HDMI cable etc ? (DotStone HDMI Audio 236) or similar if you are struggling with audio separation options.
So you end up with a HDMI splitter (1:2) and then one of the HDMI feeds goes to an Audio extractor for your sound bar etc.
Lots more wires
In a completely sane world, madness is the only freedom (J.G.Ballard).