module … not found error when the all‑in‑one loader is omitted in Lua 5.4

Goal: understand why certain Lua 5.4 distributions exclude the all‑in‑one loader from the package.searchers chain and how this omission influences the behavior when a required module cannot be located.

Because the loader’s inclusion is implementation‑defined, the exact fallback message after all searchers fail differs between builds, and developers cannot rely on a uniform error string for automated diagnostics without first inspecting the loader table.

What factors decide whether the all‑in‑one loader is present in a given Lua 5.4 build? How does its absence change the final error message when every loader in package.searchers fails? Is there a dependable way to detect the loader’s presence at runtime that does not depend on parsing the error message?