Were your details added to your mother's British passport? There is/was a section on the passport for details of children. However- if you'd been added to the passport, then there's no reason for you to have been granted Indefinite Leave to Remain on entry since this is only granted to non-British persons.
If your details were not added to the passport, but you were granted indefinite leave on arrival- then how did you get out of South Africa? Even in the early 1990s, it was not normally possible for children to travel across borders unless either included in a parent's passport or in possession of their own.
If you want to understand it better- you probably need an experienced immigration solicitor to review the papers and see what conclusions can be drawn can be made. In any case- that ILR stamp looks like your only evidence of immigration status in the United Kingdom. Keep copies in a safe place and
do not lose the original. You can do a Subject Access Request to see if there is a Home Office file- you will need any reference number on the ILR stamp.
https://www.gov.uk/government/publicati ... mmigration
It looks like under Zimbabwe law, your parents (even if they were Zimbabwe citizens) lost that status in December 1985 if they already had British citizenship on 1 December 1984.
http://www.refworld.org/docid/3ae6b4d74.html
On that basis- you do not appear to be a Zimbabwe citizen if you were born in the 1990s and if you've already got a letter from the South Africans saying you're not a citizen there then registration as a British citizen under form S2 might be the simplest solution for you.
https://www.gov.uk/government/publicati ... en-form-s2
This is not intended to be legal or professional advice in any jurisdiction.