Hi @kofoid,
I think you could do something along the lines of what you want but it might be a challenge.
In terms of the sidebar, if you had a lot of wiki pages, it would be unwieldy to list them all, but you could create a TOC with the main sections or something. The sidebar on my website in the Yada Wiki documentation area is using the TOC sidebar widget.
https://www.webtng.com/wiki/plugin-overview/
If you don’t have to change the header and footer then you can use a little HTML and CSS to customize the wiki pages by manually creating a template for it.
https://developer.www.ads-software.com/themes/template-files-section/custom-post-type-template-files/
In terms of having a different “look” for the wiki portion of the site, there are some WordPress page builders that also have some theming abilities. For example, Beaver Builder + Beaver Themer, Elementor Pro, and possibility Brizy Pro come to mind. They allow you to create headers and footers and have rules for when to show them. They also allow you to create the display template for your Post Types (in this case, the Yada Wiki post type). I’ve used Beaver Builder + Beaver Themer and Elementor Pro for things like this. Brizy Pro is still in beta and I’m not sure if there are issues for this kind of project or not. There are also Pro versions of themes, like Astra Pro and Page Builder Framework where I think you could perhaps do this using hooks, but I’ve not tried it and am not certain. All of these options are rather advanced and are paid-for options. You would be in for watching a lot of video tutorials and experimentation. If you go that route then I’d recommend having a development version of your website to work on and not do learning on your production site.
Hope this helps,
David