Connect Playstation5 with projector and soundbar?

I bought the "Epson EB-U05" projector and am actually planning to connect it to the Playstation5. Following problem:

I don't want to hear through the projector speakers, but rather through a separate soundbar, which I don't have yet. But the projector has no audio output, which means that I have to connect the soundbar directly to the PS5.

But how? The HDMI port of the PS5 is already on the projector and the PS5 does not have an optical audio output (Toslink).

Is that possible wirelessly? If so, what should I look out for when buying the soundbar and what are the disadvantages?

How about a sound receiver?

I mean, projector + PS5+ soundbar + possibly a screen already costs a 4-digit amount.

Then why only satisfy with a soundbar?

50% cool technology and 50% botch!

If so, please do the right thing: Get a smart receiver and 5.1. Speaker.

Or do you want to drive a 5-series BMW with a 120 HP diesel engine?

Certainly a good idea, but I don't know my way around so you could give an example of a model?