How can a manufacturer claim their API SP oil is backward compatible to SN+, SN, and even SL, if the amount of Zinc and Phosphorus is below 800ppm for both anti-wear metals?
Because API categories define both minimum performance standards and limits for specific elements, but they don’t require matching the old chemistry exactly, just that the oil meets or exceeds the engine protection needs of those older categories.
Here's an API-related document for your reference: https://www.infineuminsight.com/media/2841/api-engine-oil-classifications-brochure2.pdf
The latest API standards (since API SM) require the Phosphorus content to be 600~800ppm.
Older standards (API SL and SJ) require the Phosphorus to be less than 1000ppm.
So, an API SP oil with 700ppm Phosphorus, for example, would still satisfy the API SL or earlier API standards in terms of Phosphorus limit.
Also, the oil additives/formulation can be complicated. The key lies in balancing various types of additives. Lower ZDDP does not necessarily mean worse wear protection. Lake Speed Jr (The Motor Oil Geek) on YouTube has some videos about this topic.