search: lift unindexed search fallback logic

Created by: rvantonder

Stacked on https://github.com/sourcegraph/sourcegraph/pull/25495. Semantics preserving.

This puts logic that causes us to only do unindexed search one level up the call stack. It indirectly solves some issues that we may have overlooked with global searches (if we said index:no for global search I don't think it was honored before). The main benefit is extracting out state for decisions we can deal with earlier, based on the index value.

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most of the changes is just updating tests to use the upper function.