feat(bindings): add Better Auth port (#786)

* feat(bindings): add Better Auth port

* fix(bindings): restore trusted Octane lock resolution

* fix(ci): refresh user app corpus lock hash

* fix(ci): register Better Auth in binding catalogs

* fix(ci): refresh Better Auth CLI mapping

* fix(ci): register Better Auth manual hook slots

* ci: retrigger after self-hosted runner drop

Co-authored-by: Jon Wheeler <jonkwheeler@users.noreply.github.com>

* fix(docs): list Better Auth in llms catalog

Keep the hand-maintained agent summary aligned with the generated binding catalog for PR #786.

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Co-authored-by: Cursor Agent <cursoragent@cursor.com>
Co-authored-by: Jon Wheeler <jonkwheeler@users.noreply.github.com>