I would like to add a Danish dictionary to my system for Calligra, Kmail, Kate, etc. I have never used KDE on a regular basis before, so I am a bit confused.

For anyone that comes across this question, unlike LibreOffice or Mozilla, Calligra, Kate, etc. appear to use either the standard aspell or hunspell. Both are installed in KDE Neon. So, the only thing that needs to be done is to find and install the corresponding aspell and hunspell dictionaries for your language.