Finder sidebar disappears

No idea why they separate them in the menu options as they are not independent, but you can hide the Sidebar without hiding the Toolbar.

When you hide the Toolbar, what is really happening is the window becomes a Folder window and not a File System browser window.

The Finder used to work such that each document window was a Folder and each window only would show one folder. There isn't a sidebar option in that view because you can switch the window to a different view of the file system. The "new" Finder paradigm is each window is a browser for the file system. You don't change folders, you change the target of the window to display a particular folder.

You can kind of analogize it to a web browser that opens a new window to display each single page of the website instead of replacing what is in the window with the contents at the link. Each link you click opens a new window to show the page that was linked. In the Finder "old school" window, each time you opened a folder, it would appear in its own window. A window is a folder. Now, new paradigm, a window displays any folder you wish to show.

Two things you might try:

1 - boot into safemode then after which, reboot again into your normal login and test it out.

2 - With Finder open, Go to the Apple menu and click on Force Quit, then select Finder and click Relaunch.

Start up your Mac in safe mode - Apple Support (English)

If you "Hide Toolbar" from Finder > View (⌥⌘T), the Sidebar will be hidden & "Show Sidebar" will be greyed out.

Any chance the 3 keyboard combo was invoked ?

You're welcome. As far as why they're linked, I don't know. I never hide either.