The Emacs editor (plus some Emacs add-ons) might be exactly what I need.
I found an Emacs add-on called "multifiles.el" which does what I was asking about. multifiles.el worked for me in Emacs 24.3.1 in Lucid Puppy Linux 5.2.8 version 004.
These two Reddit pages mentioned multifiles.el: https://www.reddit.com/r/emacs/comments/3j1ep0/open_multiple_files_in_one_buffer
multifiles.el is available here: https://github.com/magnars/multifiles.el
I also had to download this, which multifiles.el has a dependency on: https://github.com/magnars/dash.el
In the past, I never used Emacs very much except for playing Tetris, so, it was a bit difficult to even figure out how to install and use the multifiles.el add-on.
But, the instructions for installing Emacs add-ons from https://stackoverflow.com/a/6406114 helped, even though I'm using Lucid Puppy Linux 5.2.8 version 004 rather than Windows.
I stuck all these lines in my Emacs configuration file located at ~/.emacs:
(add-to-list 'load-path "~/.emacs.d/site-lisp")
(progn (cd "~/.emacs.d/site-lisp")
( require 'multifiles)
( global-set-key [?\C-!] 'mf/mirror-region-in-multifile )
Then, I opened some of my PHP source code files, and, inside each one, typed C-x h to select all text, then typed C-! to add all the selected text to the multifile.
The changes you make to the multifile are immediately mirrored in the buffers for the original files.
You can even see the changes being mirrored while you type in the multifile, if you have both the multifile and the original file displayed at the same time using Emacs' split screen feature. (multifile.el automatically opens the multifile in the bottom pane of a split screen when you add new text to the multifile with the C-! command.)
Saving the multifile saves all the original files.
And, happily, the syntax coloring from the php-mode Emacs add-on - https://github.com/ejmr/php-mode - works properly on the multifile.
So, this will be perfect for me when (or if) I get used to Emacs, and if/when I figure out how to automate the addition of all my many source code files to the multifile, and hopefully figure out how to add some other features, like displaying the title and line number of the embedded file I'm currently working on in the multifile, reordering the embedded files, etc.
Thanks again for all the suggestions!
And, more suggestions are still welcome. Even though Emacs might (or might not) turn out to be my ultimate solution, it would still be interesting to hear of all the alternatives.
It seems like text editors with this feature are quite rare and unusual. Or maybe it's just hard to google for, because I'm not even sure what to call it except "scrivenings mode", which is what it's called in Scrivener. https://www.literatureandlatte.com/scrivener.php