Neither Hack nor Noto Mono are serif fonts (or have any serifs for that matter, except possibly for one or two letters like "I").
Are you writing the cover letter as an email in Firefox? The Font preferences in Firefox is only for text on web pages where the font is not defined or only defined as a Family (i.e., Proportional, Serif, Sans Serif, or Monospace). Whenever a web page has defined a font, then Firefox, with the help of some part of the OS, will try to match that font as exactly as possible. If you or your recipient have that font, then Firefox will display the text with that font, otherwise it will show it with the closest match. Thus even if you view some text in Noto Sans, that is no guarantee that your recipient will.
In addition, there are two formats for emails: plaintext and HTML.
If you use plaintext in your email client (e.g., gmail) then there is no support for changing the font, and it will show the text in some font that the email client decides (i.e., your recipients client will decide at his/her end).
If you use HTML in your email client, then you can change the font, and it will work like on any other web page, described above. There is support for embedding fonts in HTML, though I have never heard of that being supported for emails.
Are you writing the CV in LibreOffice? Which format? If the company wants them in
doc[x] or something similar, then it is really scary for being 2019. You (they) should be using
PDF, which will embed the font you are using in LibreOffice Writer. So no matter if they have the font or not, they will see it in that font, and the document will be as identical as possible.
LibreOffice is a Java application. It probably has a setting for GUI font and I doubt it follows KDE (Qt) font configuration. It might follow
GTK[2/3] settings though:
System Settings > Application Style > GNOME/GTK Application Style > Font. If nothing of this works and you really want to change the fonts of Java applications, then this might work.
As for the font in the document it self, it should respect whatever you choose in the font drop-down menu or set as default for the current template being used.
The fonts in the KDE System Settings dialog that you have shown are for KDE Applications (Qt), and does not apply to Firefox or LibreOffice. I would recommend against setting fonts in incorrect families (such as Sans Serif font as Monospace), it will make stuff look incorrect (monospace is used to align stuff up correctly).
Try to use PDF as much as possible since it will embed the font you use. For email try to use a popular Sans Serif font that you like and hopefully the recipient will see it closely resembling the original.