Define and document the complete public API surface

[codeforester]

Problem

The public API boundary is not fully represented in the READMEs.

Several unprefixed stdlib functions are callable but absent from the stdlib reference, including check_bash_version, dump_trace, get_my_source_dir, print_tty, safe_unalias, file logging helpers, and function enter/leave log helpers. It is therefore unclear which are supported API and which are implementation leftovers that should be private.

Four companion READMEs also point to non-existent test paths such as tests/lib_git.bats; the files live under lib/bash/<module>/tests/.

Scope

• Inventory every unprefixed function across all seven sourceable libraries.
• Document each supported public function with arguments, outputs, status, side effects, and a short example.
• Rename or otherwise classify unintentional public functions as private before the next release.
• Correct stale test paths in arg, file, git, and list READMEs.
• Add validation for README test-path references or a maintained API inventory so drift is caught.

Acceptance Criteria

• Every unprefixed supported function appears in its module README.
• Internal engines are consistently prefixed and described only where needed.
• Every documented test command/path exists and runs from the repo root.
• Top-level library summaries and module READMEs agree on the shipped surface.

Validation

• documentation/link/path validation
• ./tests/validate.sh
• git diff --check