For once, I agree with Verdy p, the correct code for the Hanja script (and only the Hanja script) is ko-Hani.
EDIT: However, I see on Hanja wikis and websites that text is written in a mix of Hangul and Hanja scripts (also the case with the word given as an example on meta), maybe we should move translations in Hangul only to ko-Hang and translations for Hanja to ko?
And it's strange that this wiki, actually uses all Korean scripts (including Hangul) everywhere in the content (I'm not speaking about the interface of the wiki itself)... So this wiki actually uses [ko-Kore] even if they want to remove Hangul (as much as possible) in favor of Hanja (I'm not really sure this is possible in modern use, unless you accept to borrow Chinese sinograms, most probably in their simplified in modern terminologies, but possibly traditional for coherence with Hanja; not sure that users will be able to read these borrowed Han sinograms, when they also are composed with phonologic traits which are appropriate to Mandarin, but most probably not for Korean).
Do you want to be inventive and create adhoc Hanjas, composed by a traditional Hanja radical and an Hangul part to replace the phonetic parts of Han sinograms? You won't be able to compose them in Unicode, so you'll fallback to use Hangul only (or maybe Latin or Cyrillic): Hangul is more complete than the basic alphabet and has many adhoc Jamos (plus a few diacritics) to compose more complex and more precise clusters that better respect the phonetic than modern Hangul which has simplified the phonology by reducing the number of jamos (the other ones being kept for historic use and encoded in Unicode even if they are not precomposable in a full syllable using a single Unicode character).
Note that Unicode contains a few clusters that don't respect the pure (L*V*T*) Hangul composition of jamos, just like Japanese has some precomposed clusters of kanas (possibly mixed with Latin, e.g. for international measurement units), and some adhoc Hanjas specific to Korean (not used in Chinese languages, Japanese, or historic Vietnamian).
I don't think we should move Korean translation made in Hangul-only to [ko-Hang]. This is their normal modern form for Korean [ko-Kore].
The use of [ko-Hang] would be ONLY to propose a transliteration to Hangul of Hanjas still normally used in modern Korean.
The interest for [ko-Hang]would be to allow a site to display Hangul easily without needing a large Han font, and it may be useful for small devices that have limited fonts
Note also that [ko-Jamo] is not needed given that encoded Hangul clusters are canonically decomposable to Jamos (so rendering on low-resolution terminals that can only display aligned (non-composed) jamos is possible algorithmically. As well this easily allows generating a romanisation fully algoithmically. Only Hanjas cause problems as they require a lookup in a possibly large dictionnary (which is not fully defined and extended regularly in successibve Unicode versions; in some cases, Hanjas do not have a well defined phonology and may turn to several distinct Hangul clusters, depending on the reader, and that's probably why some Hanjas have been kept to avoid confusions, notably for proper names).
Sorry, that's not how things work for Korean speakers. Nobody uses Hanja in their daily life in 2020. Proposal to mix Korean and Hanja in domain name got quite a lot of resist in 2018 when it was submitted to ICANN.
Hanja usage is basically now in the form of disambiguation and a hanja mania's area, and most words are expressed in Hangul. No hanja required for any expressions in Korean. We indeed borrow words in Hanja, but we display them in Korean. Nope. If they want to use Hanja in interface, they should be segregated in their own area, not in the way where you steal the Hangul's area.