You should create a partial design and use 3 components to achieve this.
For the logo you could use Image, Rich Text or Promo - for the CTA a Rich Text or Promo could also be ok. And a navigation component in the middle.
Using the grid settings will be enough to get them aligned as needed (e.g. set the logo and cta to 3 and this leaves you 6 for the ...
I don't think you can do this with the existing accordion. Luckily SXA is build very modular so you can do this with a custom version.
You need to create your own version of the accordion - create a copy of the rendering using the existing templates and view but you do need a custom controller.
For that controller, inherit Sitecore.XA.Feature.Composites....
I did some investigation and found it is caching indeed. If I clear the caches on /sitecore/admin/cache.aspx the code is triggered again (once).
As the "code:" datasources is resolved in the resolveRenderingDatasource pipeline I checked that one and saw a GetCache and SetCache processor. So yes, that data is cached. And no, the language is not part ...
If you have SXA installed, this will remove the default SiteResolver from the configuration so your config patch will not be working correctly.
Try to patch like this: