fix(openai-agents): Isolate agent run

[sentrivana]

It looks like we're running into #4718 (and probably #4690) because the different agent runs are not properly isolated. This only seems to be a problem when multiple agent runs are awaited at once (e.g. via asyncio.gather) -- it seems that leads to some scope bleed.

import asyncio

import sentry_sdk
from agents import Agent, Runner
from sentry_sdk.integrations.asyncio import AsyncioIntegration
from sentry_sdk.integrations.openai_agents import OpenAIAgentsIntegration

sentry_sdk.init(...)

main_agent = Agent(
    name="main_agent",
    model="gpt-5",
)

async def run_agent() -> None:
    runner = await Runner.run(
        starting_agent=main_agent,
        input="How are you?",
    )
    print(runner.final_output)


async def main() -> None:
    await asyncio.gather(*[run_agent() for _ in range(2)])  # throws an error
    # await asyncio.gather(run_agent())  # works

[codecov]

Codecov Report

❌ Patch coverage is 92.30769% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 84.87%. Comparing base (28d0ddd) to head (23db0c8).
⚠️ Report is 5 commits behind head on master.
✅ All tests successful. No failed tests found.

Files with missing lines	Patch %	Lines
...y_sdk/integrations/openai_agents/patches/runner.py	92.30%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4720      +/-   ##
==========================================
+ Coverage   84.84%   84.87%   +0.03%     
==========================================
  Files         156      156              
  Lines       16109    16110       +1     
  Branches     2740     2740              
==========================================
+ Hits        13667    13673       +6     
+ Misses       1655     1650       -5     
  Partials      787      787              

Files with missing lines	Coverage Δ
...dk/integrations/openai_agents/patches/agent_run.py	82.53% <ø> (ø)
...y_sdk/integrations/openai_agents/patches/runner.py	95.45% <92.30%> (+0.21%)	⬆️

... and 2 files with indirect coverage changes

[sl0thentr0py]

change looks ok in itself, don't have context on the whole integration