A rule belongs to the tab where it was added with Add rule, Staging or Production, and editing it keeps it there; a rule that matters for both is written in both. An agent that says which environment it works on is given the rules of that section as the ones to follow, at the start of its session, in planning_preflight and before each write; an agent that does not say is given both, each marked with its section.
SyncNow no longer compares the two: since version 13.2.49.74 there is no Possible drift, no check of versions and no Needs verification, because a rule is a free text with no category or version to compare. The AI check when you save a rule does not count a different rule in the other section as a conflict.
The Rules page shows one tab at a time; to read both together use Copy rules, which copies them all as text, Staging first; Copy project information, in the ... menu next to the project's name, says only how many rules each tab has, for example Staging rules: 2 and Production rules: none yet. See What is the Rules tab, and why should I write rules?.