I think it is system-wide. At least I've not encountered any input field where it doesn't work. Even Microsoft Office, which uses its own input routines, supports it.
It's a shortcut to an Edit menu item within the application, so whatever shortcut the app gives it; e.g. in Firefox it appears to be simply Cmd-<space>.
But wait... that doesn't actually work (it just switches to the next input layout). Maybe that depends on my keyboard settings in System Preferences. Or maybe it's just a Firefox bug.
Not for me. (I suspect the details of this vary between system versions, and they certainly depend on settings chosen in System Preferences / Keyboard / Shortcuts.)
It's the standard behavior. If you do something to modify or override it of course it won't work, but that's like changing the keyboard to Dvorak and saying that pressing the g key gives an i instead so you can't count on getting a g when you press the g key.
It's standard for Cocoa-based apps, I think, but it doesn't appear among the system-wide shortcuts in System Preferences on my Big Sur system, at least. The only shortcuts offered under Input Sources there are to select the previous or next input source (which are set to Cmd-Space, Cmd-Opt-Space).
A command to open the Emoji & Symbols palette is generally at the end of each application's Edit menu, and that's where its shortcut appears. But in current Firefox the item in the Edit menu shows the shortcut as Cmd-Space (not Cmd-Ctl-Space), and it doesn't work for me because the system-wide shortcut takes precedence.
If I disable that shortcut in System Preferences (which may well be the default, particularly if multiple input methods are not enabled), then Cmd-Space does work in Firefox to bring up the Emoji palette -- but note that it's not the standard Cmd-Ctl-Space combination.
Works fine for me in latest Firefox. I've never had it not work in a specific app. Though, sometimes the keyboard crashes and doesn't come back up until a restart (that could be the fault of my Ryzen Hackintosh, though).
I use two now, Quassel which is an IRC client, and QtPass which is a password manager. Both are cross-platform which is great because I don't use just Mac. I use pretty much everything. Mac, Windows, Linux, FreeBSD.
That means most of the built-in facilities of the Mac (like iCloud Keychain) are no good for me. Because they only work on Apple OSes.
But anyway both these apps don't support this. When I press the keystroke, nothing happens. I suppose it only works for apps that use the native text input boxes, or that have built specific support for the feature like browsers.
In my password manager I can do without Emoji, though it allows for text comments and it would be handy there. In IRC it's quite handy to have the option these days.
