chore(client): minor internal fixes

Author: stainless-app[bot]

Diff for: src/browserbase/_base_client.py

@@ -409,7 +409,8 @@ def _build_headers(self, options: FinalRequestOptions, *, retries_taken: int = 0
 
         idempotency_header = self._idempotency_header
         if idempotency_header and options.method.lower() != "get" and idempotency_header not in headers:
-            headers[idempotency_header] = options.idempotency_key or self._idempotency_key()
+            options.idempotency_key = options.idempotency_key or self._idempotency_key()
+            headers[idempotency_header] = options.idempotency_key
 
         # Don't set these headers if they were already set or removed by the caller. We check
         # `custom_headers`, which can contain `Omit()`, instead of `headers` to account for the removal case.
@@ -943,6 +944,10 @@ def _request(
         request = self._build_request(options, retries_taken=retries_taken)
         self._prepare_request(request)
 
+        if options.idempotency_key:
+            # ensure the idempotency key is reused between requests
+            input_options.idempotency_key = options.idempotency_key
+
         kwargs: HttpxSendArgs = {}
         if self.custom_auth is not None:
             kwargs["auth"] = self.custom_auth
@@ -1475,6 +1480,10 @@ async def _request(
         request = self._build_request(options, retries_taken=retries_taken)
         await self._prepare_request(request)
 
+        if options.idempotency_key:
+            # ensure the idempotency key is reused between requests
+            input_options.idempotency_key = options.idempotency_key
+
         kwargs: HttpxSendArgs = {}
         if self.custom_auth is not None:
             kwargs["auth"] = self.custom_auth