Deprecated doesn't mean deleted, it just means "no longer updated/developed with a goal towards removal".
Not sure why would you want a single-process OS on modern hardware, but there are some alternatives that run much less things on the background than regular Linux: Haiku, FreeBSD, NetBSD, OpenBSD, or some lightweight non-glibc, non-systemd Linux-based like Adelie or Alpine.
Otherwise, this is accurate.
It won't fork random processes you don't explicitly tell it to. I thought it was obvious that if you don't want unsolicited processes, then don't specify /bin/init as /bin/foo. The practical example is /bin/sh, but it could be any other executable.
Up to you to specify a binary that does what you want, and doesn't require a bunch of other processes like gdbus to function itself.
init=/bin/sh is more or less like ms-dos loading command.com
Give me a date, and I will tell you what existed.
Nothing mainstream existed until windows 3.1. at least on x86/32
There also was OLEC on windows 2, that did run in real mode, but the only thing that took advantage of it was the demos, and samples: no commercial product used it.
My point was that running your own chosen process as PID1 (or, to be more practical, a minimal init or maybe system v init with single entry for process to run) matches the requirements of running small set of processes just as well as DOS (if you need more, it's IMO more worthwhile to start getting a build of some RTOS for your platform)