I'm not overly familiar with Plan 9, but a significant advantage of the filesystem as an API is that it composes well. You can put any service inbetween that consumes the existing file and provides a new file with the same API contract, but different behavior (e.g. a /dev/screen that's cropped to a certain area, or that inverts colors on everything drawn into it). Then you can make a new mount namespace where the new file is put in the place of the old file, so that the actual process consuming it has no idea that someone is sitting in the middle. With a traditional shared object, you'd have to engage in LD_PRELOAD shenanigans to achieve the same, or if the library is statically linked and does not have any hooks, you're straight out of luck.

[From memory, so take with a grain of salt]

a) tooling and familiarity

b) it's leveraged for modularity, composition and access control. Normal unix basically has no modularity and little composition beyond piping to stdin (which is of limited applicability). And of course no useful access control mechanism to speak of. The last 5 decades mostly just added layers of shitty hacks that don't work and that no one understands anymore (by contrast e.g. the original unix ownership and permissions model was misdesigned but at least possible to grasp).

Plan9 does substantially better in both regards via clever use of a proper union file system (which incidentally makes another horrible hack superfluous: symlinks). If you want your shell, or some other executable, to find some executable, you mount it into its /bin -- there is no $PATH. If you want some process or user to have access to a resource (file, device, server in the network, ...) you mount it into their filesystem. This gets rid of a lot of problems and special purpose solutions.

An advantage is, you don't need any API or function calls. You can inspect or manipulate anything from the shell ad lib using cat, echo, and the usual commands. Plan 9 doesn't have ioctl() calls because it's not meaningful to send pointers across the network. Instead each device and service provides a file called cntrl (or something similar) to which you can read or write text - using cat, echo etc. So it's easy to write small test scripts or even whole applications, in the shell or any language you like.

Functionally it's the same. The functions called could live in the kernel (a system call), in the process itself or in a shared lib loaded into the process address space.

Interpreting bytes is message passing and this communication happens through the handle/descriptor to the file/object/whatever. As above, this handle could have come from the kernel, another process or the executing process itself (the process opened some file or whatever).

I think the message passing version happening through a handle can be more versatile as you could send this handle over to another process. Could copy it and distribute it to other processes in a easier way than injecting/changing a (presumably C ABI) into a process address space.

Well, as I said, one advantage is that processes running on the CPU server can access your local files transparently—including /dev/screen, /dev/mouse, and /dev/bitblt, if you so choose.

That means you can run graphical applications on the CPU server.