feat: adding gpt 5.1 to stagehand (#1264)

# why

we want to benchmark/use the sota models in stagehand

# what changed

added gpt 5.1 to available models, setting reasoning to low for gpt 5.1
specifically since it cannot be set to minimal.

# test plan

---------

Co-authored-by: Miguel <36487034+miguelg719@users.noreply.github.com>

Author: Kylejeong2

.changeset/bright-meals-add.md

@@ -0,0 +1,5 @@
+---
+"@browserbasehq/stagehand": patch
+---
+
+feat: adding gpt 5.1 to stagehand

packages/core/lib/v3/llm/aisdk.ts

@@ -127,6 +127,7 @@ export class AISdkClient extends LLMClient {
 
     let objectResponse: Awaited<ReturnType<typeof generateObject>>;
     const isGPT5 = this.model.modelId.includes("gpt-5");
+    const isGPT51 = this.model.modelId.includes("gpt-5.1");
     if (options.response_model) {
       try {
         objectResponse = await generateObject({
@@ -138,7 +139,7 @@ export class AISdkClient extends LLMClient {
             ? {
                 openai: {
                   textVerbosity: "low", // Making these the default for gpt-5 for now
-                  reasoningEffort: "minimal",
+                  reasoningEffort: isGPT51 ? "low" : "minimal",
                 },
               }
             : undefined,

packages/evals/lib/AISdkClientWrapped.ts

@@ -133,6 +133,7 @@ export class AISdkClientWrapped extends LLMClient {
 
     let objectResponse: Awaited<ReturnType<typeof generateObject>>;
     const isGPT5 = this.model.modelId.includes("gpt-5");
+    const isGPT51 = this.model.modelId.includes("gpt-5.1");
     if (options.response_model) {
       try {
         objectResponse = await generateObject({
@@ -144,7 +145,7 @@ export class AISdkClientWrapped extends LLMClient {
             ? {
                 openai: {
                   textVerbosity: "low", // Making these the default for gpt-5 for now
-                  reasoningEffort: "minimal",
+                  reasoningEffort: isGPT51 ? "low" : "minimal",
                 },
               }
             : undefined,