chore(docs): Remove explicit openai agents integration registration (#14718)

## DESCRIBE YOUR PR
This PR updates the documentation for the `OpenAIAgentsIntegration` to
reflect that it is automatically registered when the `agents` package is
detected.

The documentation examples have been simplified to remove explicit
`OpenAIAgentsIntegration()` setup from `sentry_sdk.init()`, aligning
with the goal of providing an "out-of-the-box" experience for AI
observability.

An "Options" section has been added, similar to other AI integrations,
to explain when explicit registration is still useful (e.g., to
configure options like `include_prompts`).

## IS YOUR CHANGE URGENT?  
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- [x] None: Not urgent, can wait up to 1 week+

## SLA

- Teamwork makes the dream work, so please add a reviewer to your PRs.
- Please give the docs team up to 1 week to review your PR unless you've
added an urgent due date to it.
Thanks in advance for your help!

## PRE-MERGE CHECKLIST

*Make sure you've checked the following before merging your changes:*

- [ ] Checked Vercel preview for correctness, including links
- [ ] PR was reviewed and approved by any necessary SMEs (subject matter
experts)
- [ ] PR was reviewed and approved by a member of the [Sentry docs
team](https://github.com/orgs/getsentry/teams/docs)

## LEGAL BOILERPLATE

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-->

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in the State of Delaware in 2015 as Functional Software, Inc. and is
gonna need some rights from me in order to utilize my contributions in
this here PR. So here's the deal: I retain all rights, title and
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contributions, under Sentry's choice of terms.

## EXTRA RESOURCES

- [Sentry Docs contributor guide](https://docs.sentry.io/contributing/)

---
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Co-authored-by: Cursor Agent <[email protected]>

Author: vgrozdanic

docs/platforms/python/integrations/openai-agents/index.mdx

@@ -30,23 +30,9 @@ uv add "sentry-sdk"
 
 ## Configure
 
-Add `OpenAIAgentsIntegration()` to your `integrations` list:
+If you have the `agents` package in your dependencies, the OpenAI Agents integration will be enabled automatically when you initialize the Sentry SDK.
 
-```python
-import sentry_sdk
-from sentry_sdk.integrations.openai_agents import OpenAIAgentsIntegration
-
-sentry_sdk.init(
-    dsn="___PUBLIC_DSN___",
-    traces_sample_rate=1.0,
-    # Add data like inputs and responses to/from LLMs and tools;
-    # see https://docs.sentry.io/platforms/python/data-management/data-collected/ for more info
-    send_default_pii=True,
-    integrations=[
-        OpenAIAgentsIntegration(),
-    ],
-)
-```
+<PlatformContent includePath="getting-started-config" />
 
 ## Verify
 
@@ -57,8 +43,6 @@ import asyncio
 import random
 
 import sentry_sdk
-from sentry_sdk.integrations.openai_agents import OpenAIAgentsIntegration
-
 import agents
 from pydantic import BaseModel  # installed by openai-agents
 
@@ -79,14 +63,11 @@ random_number_agent = agents.Agent(
 
 async def main() -> None:
     sentry_sdk.init(
-        dsn="...",  # same as above
+        dsn="___PUBLIC_DSN___",
         traces_sample_rate=1.0,
         # Add data like LLM and tool inputs/outputs;
         # see https://docs.sentry.io/platforms/python/data-management/data-collected/ for more info
         send_default_pii=True,
-        integrations=[
-            OpenAIAgentsIntegration(),
-        ],
     )
 
     await agents.Runner.run(
@@ -109,7 +90,36 @@ Data on the following will be collected:
 - number of input and output tokens used
 - LLM models usage
 
-Sentry considers LLM and tool inputs/outputs as PII and doesn't include PII data by default. If you want to include the data, set `send_default_pii=True` in the `sentry_sdk.init()` call.
+Sentry considers LLM and tool inputs/outputs as PII and doesn't include PII data by default. If you want to include the data, set `send_default_pii=True` in the `sentry_sdk.init()` call. To explicitly exclude prompts and outputs despite `send_default_pii=True`, configure the integration with `include_prompts=False` as shown in the [Options section](#options) below.
+
+## Options
+
+By adding `OpenAIAgentsIntegration` to your `sentry_sdk.init()` call explicitly, you can set options for `OpenAIAgentsIntegration` to change its behavior:
+
+```python
+import sentry_sdk
+from sentry_sdk.integrations.openai_agents import OpenAIAgentsIntegration
+
+sentry_sdk.init(
+    # ...
+    # Add data like inputs and responses;
+    # see https://docs.sentry.io/platforms/python/data-management/data-collected/ for more info
+    send_default_pii=True,
+    integrations=[
+        OpenAIAgentsIntegration(
+            include_prompts=False,  # LLM and tool inputs/outputs will be not sent to Sentry, despite send_default_pii=True
+        ),
+    ],
+)
+```
+
+You can pass the following keyword arguments to `OpenAIAgentsIntegration()`:
+
+- `include_prompts`:
+
+  Whether LLM and tool inputs and outputs should be sent to Sentry. Sentry considers this data personal identifiable data (PII) by default. If you want to include the data, set `send_default_pii=True` in the `sentry_sdk.init()` call. To explicitly exclude prompts and outputs despite `send_default_pii=True`, configure the integration with `include_prompts=False`.
+
+  The default is `True`.
 
 ## Supported Versions
 

docs/product/insights/ai/agents/getting-started.mdx

@@ -172,17 +172,13 @@ The Sentry Python SDK supports OpenAI Agents SDK.
 
 ```python
 import sentry_sdk
-from sentry_sdk.integrations.openai_agents import OpenAIAgentsIntegration
 import agents
 from pydantic import BaseModel
 
 sentry_sdk.init(
     dsn="YOUR_DSN",
     traces_sample_rate=1.0,
     send_default_pii=True,  # Include LLM inputs/outputs
-    integrations=[
-        OpenAIAgentsIntegration(),
-    ],
 )
 
 # Create your AI agent