Presently, due to a limitation in document representation (the specification is called OASIS ODF), you can’t add a note in a note. Since Zotero does its own management through macros and doesn’t “collaborate” with ODF, perhaps this could be done but according to your trials it seems very unlikely.
What do you call the footer?
In Writer parlance, the footer is an area at bottom of page distinct from main text area. The footer is repeated the same on every page.
The main area is where you write your discourse. Footnotes are displayed at bottom of the main area. They belong in the main area but are handled specifically (they are recorded at the point of occurrence: the anchor point, and their layout is deferred until Writer has computed the size needed to hold note contents. Notes are part of the main text area.
Consequently, you can write by yourself in the note area because it is dynamically created outside your control.
Although I have seen examples of notes in notes, you should think twice about the significance. If this note-in-note is strongly related to the note, perhaps it should become just another paragraph for the current note (and therefore be referenced with the original note number). It is easy to do it in standard Writer note: just add another paragraph. I don’t know how this can be done with Zotero because I have no experience with it.
A problem arises if the note-in-note is shared among several “primary” notes and you want to reference it.
Another approach is to consider your anchor point has two notes: the primary one and the “note-in-note”. You can always attach as many notes as you want to any anchor point. This moves the referencing number from the note to the text. This may be an acceptable workaround.
When asking here, always mention OS name, LO version and save format.