Question: After swapping my language and input options about (UK layout and German layout) to support the two keyboards I have, a certain key will stop working partially depending on the layout.

If I swap my input method to UK, the apostrophe/at-sign key will stop working. Windows 10 will make a tone sound when pressed twice, and if held it will input many of that key, as should be the case.

If I swap the the DE layout, the would-be apostrophe key works fine, but the colon/semicolon key (Ö on the German keyboard) stops working unless held.

I'm certain it's not a hardware issue, it must be to do with Windows 10.  

What's going on and how do I fix it?

Answer: 
I solved this by removing a mistakenly added 'change layout' shortcut, to the grave (`) key, oddly affecting the apostrophe and ö keys on the other layouts.

To fix this:

* Context-menu/Right-mouse on the Language Bar on the Windows taskbar
-> Settings/Einstellungen
* In the third section, "Change the Input Method"/"Wechseln der ingabemethode", open the blue link at the bottom, "Change the shortcut keys for the Language Bar"/"Abkürzungstasten der Sprachenleiste ändern"
* From there,
remove the setting for "Change Input Language"/"Zwischen
Eingabesprachen" from whatever it is (mine was Graviszeichen (`)) to
None.
I hit the exact same issue (`Ö` only working when held down) and I somehow stumbled across this question, so I wanted to post an answer with the current method to remove these shortcuts in Windows 10 version 2004:

* Go into Settings > Time & language > Language > Keyboard > Input language hot keys
* Select "Between input languages" then click "Change Key Sequence..." (even if it says "(none)" under "Key sequence" in the table it might still be assigned!)
* Make sure in the dialog that opens that none of them is set to "Grave Accent (`)".  
If it is, change it to "Not Assigned" and press OK.

Your `Ö` key should be back to functioning again