docs: rename CLAUDE.md to AGENTS.md and rebrand provider-agnostic

Delete CLAUDE.md in favor of AGENTS.md as the orientation doc, rebrand
the project from Codex-bottle to provider-agnostic bot-bottle, and
repoint every CLAUDE.md reference across PRDs, research notes, the
implementer agent example, and the yaml_subset comment.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

docs/prds/0011-per-file-md-manifest.md

@@ -24,7 +24,7 @@ no `bottles/` subdirectory, period.
 The YAML we accept is bounded (flat keys → strings, lists, simple
 nested dicts), so the parser is hand-rolled and stdlib-only — no
 PyYAML dependency. The project's "low deps by default" stance
-(CLAUDE.md) stays intact.
+(AGENTS.md) stays intact.
 
 ## Problem