After a lot of searching around online trying to figure this one out, I found that if you have the annoying language bar in Windows 11 displayed in the corner of your screen but Windows insists you only have one language installed, you can get rid of it with a few Windows PowerShell commands.
First off, open a PowerShell window and type the following:
Get-WinUserLanguageList
On my system the following is returned:
Ironically, Windows reports that the language I want is the only one installed on the system, even though the language bar still displays the US English keyboard layout.
To instantiate a single copy of the desired language on the language list, and therefore remove the language bar, use the New-WinUserLanguageList function with the LanguageTag from the function above. In my case that's en-GB. If you only wanted the US layout you'd type en-US, for example:
$1 = New-WinUserLanguageList en-GB
After this, type the code snippet below, and the language bar will suddenly and unceremoniously vanish from your taskbar:
Set-WinUserLanguageList $1
I recommend restarting at this point, and the language bar should be gone (at least until an update occurs that re-introduces the bug).