The trick is to hide in plain sight. Call your process “tracker-miner-fs” (common suspiciously named GNOME process”). When the system administrator sees your process eating up huge amount of CPU time and does a web search, they’ll come to the conclusion it’s just GNOME being GNOME.
Signed, greybeard gnu/linux admin who hates procs like that!
edit: this is also why lsof, ss, strace, and bpftrace etc., are helpful
mount is a bit harder (as its calls into code that is more in the core kernel fs code, but one can just reimplement it oneself, to filter out the mounts you don't want to show.
A sysadmin just would see . . .. as directory entries.
How did chroot used to work in this regard? Were mountpoints outside the chroot jail itself accessible? Because if so, that ... would violate some key points of using a chroot jail in the first place. Though if chroot applied strictly to the filesystem and not mount points that might still offer benefits, and I seem to recall running into ... unexpected behaviours ... using chroots in the past.
If an unconstrained uid zero process is inside the chroot but can access or create device nodes, it can mount devices within the chroot just fine.
When your application calls open() or read() or stat() or whatever, it passes through libc and then makes a syscall to ask the kernel "hey, give me a file handle for /proc/foo", "hey, give me the first 500 bytes from this file handle", etc. Then in the kernel, that syscall triggers a function that figures out what filesystem you're talking to and passes the request to that filesystem driver. AFAIK, the procfs driver just reads (and writes) a bunch of data structures in kernel memory and passes the result through as a filesystem. So the actual underlying data structure does always exist and is a hard requirement for the system to work, but procfs is just a userspace view into that underlying data in the kernel. Incidentally sysfs would be the same - the stuff you see in /sys exists in the kernel regardless, but the kernel doesn't really care whether those data structures are exposed to userspace as a virtual filesystem.