Better living through reliability.
The background section of a postmortem explains unobvious, nuanced, or unexpected technical details about a system or process.
It should not be used to explain how the root cause or resolution was determined, the order of troubleshooting, technical red herrings, escalations that happened, etc.
Unless the background section is required reading to understand the executive summary, the root cause and resolution, and the impact sections, the background section should go below all of them.
Sometimes wrong turns, bad assumptions, and red herrings are useful to communicate in the postmortem, but should be considered secondary to the goal of communicating as clearly as possible the primary issue and resolution at hand and educating everyone to better understand the system. Better places to call those things out would be in the "What Went Wrong" section, or perhaps even in it's own section towards the end of the postmortem. Unless those additional bits of information are issues themselves that need to be addressed (and thus should be added as action items to the postmortem), they may not need to be included in the postmortem at all.