The only thing I've found impacting this, is when you specifically use the "Ultra" thinking/reasoning effort, then codex adds a small part to the system prompt to further get the model to use sub-agents. Any other reasoning/thinking effort than "Ultra" and this piece is no longer in the system prompt.

Seemingly mostly a prompting thing it seems on the surface. GPT-5.5 (and maybe even GPT-5.4) already had (experimental?) support for sub-agents, remember using it even with -spark which I think was launched together with GPT-5.4 if I remember correctly, so this whole "use sub-agents" stuff most have been part of the training data for quite some time already, but maybe they've mainly been iterating on the prompt themselves since then.