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/utils/claudeInChrome/mcpServer.ts

@@ -181,8 +181,6 @@ export function createChromeContext(
         usage?: { input_tokens: number; output_tokens: number }
       }> => {
         // sideQuery handles OAuth attribution fingerprint, proxy, model betas.
-        // skipSystemPromptPrefix: the lightning prompt is complete on its own;
-        // the CLI prefix would dilute the batching instructions.
         // tools: [] is load-bearing — without it Sonnet emits
         // <function_calls> XML before the text commands. Original
         // lightning-harness.js (apps repo) does the same.
@@ -193,7 +191,6 @@ export function createChromeContext(
           max_tokens: req.max_tokens,
           stop_sequences: req.stop_sequences,
           signal: req.signal,
-          skipSystemPromptPrefix: true,
           tools: [],
           querySource: 'chrome_mcp',
         })