TriggerChatTransport, AgentChat, and chat.createStartSessionAction now
accept a string-or-function baseURL so callers can route per endpoint —
e.g. .in/append through a trusted edge proxy while keeping .out SSE
direct. The same surfaces add a fetch override for header injection,
custom retries, or proxy rewrites that go beyond URL routing; SSE GETs
are covered via a new fetchClient option on SSEStreamSubscription.

streamBaseURL on TriggerChatTransport is kept as a backwards-compat
alias and continues to win for the "out" endpoint when set. Plain-string
baseURL still applies to every endpoint, matching prior behavior.

Reference example for the trusted-edge-signals pattern. A minimal
Cloudflare Worker (references/ai-chat/cf-worker) rewrites POST
/api/v1/sessions and POST /realtime/v1/sessions/{id}/in/append to
inject server-trusted bot-management signals into payload.metadata.__cf
before forwarding upstream. The new cfTrustTestAgent declares the
namespace in clientDataSchema and echoes the values back so the
round-trip is visible in the streamed response.

cf-worker README walks through the wire-up and shows the function-form
baseURL snippet for routing .out SSE direct while .in/append flows
through the worker.

…est input in SSE wrapper

When chat.createStartSessionAction was given a baseURL or fetch
override, the inline POSTs for /api/v1/sessions and
/api/v1/auth/jwt/claims forgot to forward apiClientManager.branchName as
the x-trigger-branch header. Callers running against a preview branch
(via TRIGGER_PREVIEW_BRANCH or VERCEL_GIT_COMMIT_REF) would route to
the wrong environment in override mode. Extracted the header builder
to a shared helper.

The SSE fetch wrappers in TriggerChatTransport.subscribeToSessionStream
and AgentChat.subscribeToSessionStream cast to typeof fetch but coerced
non-string input via .toString(), which yields "[object Request]" on
Request objects and discards the Request's intrinsic method/headers/
signal. Replaced the coercion with explicit branches for string, URL,
and Request — Request inputs now extract url + init properly with any
caller-provided init taking precedence (matches fetch(Request, init)
semantics).

When AgentChat.appendInputChunk fails non-2xx after the inline-POST
refactor, it was throwing a plain Error. Callers of sendRaw, sendMessage,
sendHandover, and sendHandoverSkip inspecting error.name ===
"TriggerApiError" or error.status saw "Error" / undefined instead of
the values the prior ApiClient/zodfetch path produced. Synthesize the
same shape here so the public error contract is preserved. Matches the
equivalent fix already applied to TriggerChatTransport.