> I'm almost certain it stood for "Betriebssystem 2000" originally (Betriebssystem being German for operating system), which is so quaint

Indeed it does. In fact, Siemens used to also sell BS1000 and BS3000.

BS3000 was a rebranding of Fujitsu's MSP operating system. Fujitsu claimed that MSP was a "clone" of IBM MVS, but it turned out that they'd actually stolen a lot of the copyrighted MVS source code from IBM and made minor changes to try to hide the theft. When IBM sued Fujitsu, Siemens stopped selling BS3000; Fujitsu ended up having to pay IBM hundreds of millions in damages (and Hitachi too, who were doing the same thing independently). I don't know if IBM sued Siemens, they may have accepted their claims that they didn't know the code was stolen and were a victim of Fujitsu's lies about its origin.

Both BS2000 and BS3000 were for IBM S/370-compatible mainframe hardware (albeit only partially compatible in the case of the BS2000 machines). But while BS3000 was an illegal copy of MVS, BS2000 was a completely incompatible operating system, which Siemens had bought from RCA, being originally RCA's TSOS operating system for its RCA Spectra 70 mainframe line. Siemens' mainframe business started out first by reselling and then by licensing RCA's, but ended up surviving a lot longer than RCA's did. Like Siemens' mainframes, the Spectra 70 was compatible at the instruction set level (at least for unprivileged code, there were some incompatibilities in privileged instructions), but had an incompatible operating system–in fact the first Siemens mainframes were just rebadged RCAs, but later Siemens went on to design their own machines. Another vendor who copied the IBM S/370 ISA but with an incompatible OS was Wang (with their Wang VS machines).

BS1000 was a lower-end operating system for the same hardware, I don't know much about it. It was for the Siemens 4004, which was a rebadged RCA Spectra 70. Random fact, the computer shown in the 1971 film "Willy Wonka and the Chocolate Factory" was a Siemens 4004.

In 1990, Siemens ended up buying Nixdorf, who had their own line of operating systems for clone IBM mainframes, which Nixdorf had acquired by buying the US firm TCSC in 1980. However, shortly before the Siemens acquisition, Nixdorf decided to kill its own IBM mainframe clone business, because it wanted to focus on Unix instead. And then in 1999, Siemens transferred their computing business to a joint venture with Fujitsu, and then 10 years later Fujitsu bought Siemens out, so now BS2000 belongs to Fujitsu. BS1000 and BS3000 died years ago. Fujitsu also has the ICL VME (aka OpenVME) operating system they got by buying the UK mainframe manufacturer ICL, and they still have MSP, their stolen copy of MVS – IBM agreed they could keep on selling it in Japan if they paid compensation and licensing fees to IBM. But while Fujitsu MSP still exists in Japan, it is stuck in the 1980s, it hasn't received any new features IBM introduced post-1990, and Fujitsu never managed to keep up with IBM's advances. In 2001, MVS (or OS/390 as it had been effectively rebranded) went from 31-bit to 64-bit addressing and in the process became z/OS; Fujitsu MSP is stuck on 31-bits. (Yes, not 32, 31–IBM decided to reserve a bit for use as a flag in every memory address.)