fix: disable experimental API betas by default, reduce side query token usage, standardize Headers type (#281)

* fix: disable experimental API betas by default to prevent 500 errors

Tool search (defer_loading), global cache scope, and context management
betas require internal Anthropic server-side support. External accounts
receive 500 Internal Server Error when these are sent.

Set CLAUDE_CODE_DISABLE_EXPERIMENTAL_BETAS=true by default in the CLI
entrypoint. Users with internal access can opt back in with =false.

Also includes: cache key stability fixes (Sonnet 1M latch, system-before-
messages key ordering, resume fingerprint isMeta skip), sideQuery default
cleanup, and /dream command.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

* refactor: standardize API headers to Headers type and enable tengu feature flags by default

* fix: address PR review — dream lock, MCP betas guard, redundant Partial

- Call recordConsolidation() programmatically in /dream instead of
  delegating to model prompt (unreliable)
- Add CLAUDE_CODE_DISABLE_EXPERIMENTAL_BETAS guard to MCP entrypoint
  (was only in CLI entrypoint, causing 500s in MCP server mode)
- Remove redundant ? markers from SecretValueSource Partial<{}> type

---------

Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

src/tools/AgentTool/prompt.ts

@@ -60,7 +60,7 @@ export function shouldInjectAgentListInMessages(): boolean {
   if (isEnvTruthy(process.env.CLAUDE_CODE_AGENT_LIST_IN_MESSAGES)) return true
   if (isEnvDefinedFalsy(process.env.CLAUDE_CODE_AGENT_LIST_IN_MESSAGES))
     return false
-  return getFeatureValue_CACHED_MAY_BE_STALE('tengu_agent_list_attach', false)
+  return getFeatureValue_CACHED_MAY_BE_STALE('tengu_agent_list_attach', true)
 }
 
 export async function getPrompt(