But where was this step really done? Where became protected mode the norm and real mode something for old people with fond memories?
My understanding is it was a gradual transition, spanning a decade. I would consider the start of the transition for typical PC users to be the release of Windows 3.0 in 1990 and the culmination of the transition to be the release of windows XP in 2001.
Windows 3.0 made use of protected mode to expand the memory available for windows applications. The win16 programming environment had originally been designed to run in real mode, but the way it handled memory management meant that windows programs were generally amenable to running in protected mode without being recompiled.
Specifically windows 3.0 had three modes. "real mode" as the name suggests ran the CPU in real mode, the same as previous versions of windows. "standard mode" used the protected mode features of the 286 to provide access to more memory. "enhanced mode" further used the features of the 386 to support virtual memory and to allow running multiple DOS applications at the same time.
For DOS applications, AFAIK 16 bit protected mode was little used, however 32-bit protected mode was used through "DOS extenders". Most famously DOS/4GW bundled with Watcom C++. Most of the later DOS games used DOS/4GW.
As well as supporting native windows applications in protected mode, windows 3.0 and later offered an interface called DPMI. This interface allowed DOS extenders to cooperate with windows and thus allowed protected mode DOS applications to run under windows.
However, while windows 3.0 used protected mode it did not use it exclusively. The system still had to switch back to real mode to call into DOS and the BIOS. Windows 3.1, released in introduced "32-bit disk access" and "32-bit file access" to reduce the number of times windows would have to switch back to real mode. The ability to switch back down to DOS was kept around for backwards compatibility. In 1993, "win32s" was released, allowing windows 3.1 and windows 3.11 to support 32-bit applications.
Windows 95 moved even more stuff to 32-bit mode, but it's heritage as a DOS based single user operating system was still clearly visible. Windows 95 would try to use 32-bit drivers where possible, but was still able to switch to 16 bit where needed.
Windows NT on the other hand was designed from the ground up as a multiuser operating system and on x86 it always ran in 32-bit protected mode. You had to have 32-bit drivers for your hardware, calling out to DOS was not an option. Linux too was designed from the start as a protected mode operating system running on the 386.
So in the late 1990s, MS had two linages of operating system for the PC. 9x was what most home users and smaller businesses got, NT had proper multi-user support and was more robust, but lacked support for "plug and play" and had relatively poor support for legacy software.
Windows 2000 had been intended to be a unifying release, abandoning the windows 9x series. However in the end only "professional" and "server" editions of windows 2000 were released. Home users were instead treated to a final upgrade to the windows 9x series in the form of windows ME.
Windows XP finally unified the lineup, and deprecated the old DOS-based versions of windows.