I definitely don't misunderstand what swap is for. I've implemented swap for a hobby os.
Swap is absolutely "more RAM" in layman's terms. If you NEED 10GB of memory to have open everything you want on your machine, but you only have 8GB of RAM, swap will make that happen for you. Now ideally the OS is using this for inactive pages (those programs you have open but you aren't actually using), and the nuance to how swap can be used to make the RAM you do have more effective is an interesting attribute of swap (another commenter mentioned swap being used as temporary storage to defrag the physical memory), but every single reference you linked says the same thing - swap is for when you need more memory than you have physical memory for.
You seem to be conflating swaps features with it being anything other than an extension of your physical memory. The primary use of swap is to enable a virtual memory space that is larger than the available physical memory. That can be leveraged for smarter things than "store page with the oldest access time" but fundamentally swap is to enable using more memory than you have more physical memory for. Yes, you can ramp your swappiness and have the OS be more aggressive about paging to disk, this is silly if you have so much unused RAM as the performance implication of a page fault and retrieval from disk is huge.
From your links:
https://help.ubuntu.com/community/SwapFaq: "Swap space is used when your operating system decides that it needs physical memory for active processes and the amount of available (unused) physical memory is insufficient." -> More RAM for your memory heavy usage. In this case if you buy more physical RAM your programs will run faster.
https://docs.redhat.com/en/documentation/red_hat_enterprise_...: "The swap space acts as an extension to the physical memory and allows the system to continue running smoothly even when physical memory is exhausted." and "Swap space in Linux is used when the amount of physical memory (RAM) is full. If the system needs more memory resources and the RAM is full, inactive pages in memory are moved to the swap space." -> More RAM. Slow RAM, but more.
https://wiki.archlinux.org/title/Swap#Swappiness: "Swapping is the process whereby a page of memory is copied to the preconfigured space on the hard disk, called swap space, to free up that page of memory. The combined sizes of the physical memory and the swap space is the amount of virtual memory available." -> Do I need to repeat myself here?
Did you seriously write and link all of that without reading any of it?