You can do this with any two layered backgrounds - an image of the wood and the SVG on top of it.
To get the responsive behaviour to work I think it is mainly just a case of making your white SVG a suitable width so that it doesn’t collide with the headline.
Everything else on the page can in front of the image and SVG so there is no complex layering or overlapping to worry about.
The only real question is the behaviour on small screens when the content stacks - I would just use a different SVG image for that and swap it in at a breakpoint.
Here is a very simple way to do it with just a SectionsPro with a background (image) and overlay (SVG) - The image is from unsplash and the SVG is a crude copy of your example made in Affinity designer in about 2 minutes. I’m sure there are tons of other stacks that you could use to layer two images if you prefer.
You just need to add a column stack to contain your text on the left and logo on the right.
Again, in this instance, the key is drawing the SVG to be a shape that works. Keep the web side of things simple.
Remember - nothing will show in this example until you add some content to the section, there background has no height without content.