Archival documents and collections content is not presented in the APA 7th Manual, and can only be found on the APA Style website under the Style and Grammar Guidelines section.
Referring to the information on the Archival Documents and Collections page (see link below), you should consider combining the examples of a 'letter from a repository' with the 'letter from a private collection' (the latter just for the transcription element). The citation elements would be:
Authors: Lingiari, V., Manguari, P., Ngalgardji, G., & Kitgnaari, L-J..
Date: 1967, April 19
Title: [Petition to Lord Casey (Hardy, F. J. & Jeffrey, J. W., Trans.)].
Source: National Museum Archive
Location: https://www.nma.gov.au/__data/assets/pdf_file/0007/698308/petition-to-lord-casey.pdf
For a full explanation of why the title for example appears this way, please see the link provided.