[CLEAN] Synthetic Benchmark PR #20160 - Add arun_deployment and replace @sync_compatible with @async_dispatch

[tomerqodo]

Benchmark PR PrefectHQ#20160

Type: Clean (correct implementation)

Original PR Title: Add arun_deployment and replace @sync_compatible with @async_dispatch
Original PR Description: Related to PrefectHQ#15008

This PR is needed for the Custom Deployment SDK feature (see plans/2026-01-06-custom-deployment-sdks.md).

Summary

• Add arun_deployment as an explicit async function for running deployments
• Replace @sync_compatible with @async_dispatch on run_deployment
• run_deployment now automatically dispatches to arun_deployment in async context
• Sync context uses SyncPrefectClient directly (no event loop magic)
• Export arun_deployment from prefect.deployments

Changes

The run_deployment function now uses the @async_dispatch pattern instead of @sync_compatible:

# Async context - dispatches to arun_deployment
async def my_flow():
    flow_run = await run_deployment("my-flow/my-deployment")

# Sync context - runs synchronously with SyncPrefectClient
def my_sync_code():
    flow_run = run_deployment("my-flow/my-deployment")

# Explicit async - can also call arun_deployment directly
async def explicit_async():
    flow_run = await arun_deployment("my-flow/my-deployment")

Backward Compatibility

• The run_deployment signature is maintained
• The run_deployment.aio attribute is preserved, pointing to arun_deployment
• All existing tests continue to pass

🤖 Generated with Claude Code
Original PR URL: PrefectHQ#20160