The Verdict: Not eligible
At 25 or over, the exchange visa's work limb is closed to you, because the age limit is in the statute. Look at Skilled Migration or Digital Nomad instead.
The limb is for a foreigner 'who is under 25 years of age', tested when the visa is issued, with no discretion. It is also narrower than overseas working holidays: one employer, one year, and a two-year bar on permanent residence afterwards.
Skilled Migration: since October 2024 work visas need 100 points, and an occupation on the critical skills list scores all 100 by itself. That route leads to permanent residence after five years.
Digital Nomad: if you work remotely for an employer outside South Africa and earn at least R1 million a year, the remote work visa runs for up to three years.
If you are on an exchange programme run by a government body or a learning institution, that separate limb of the exchange visa has no age limit.