Add arun_deployment and replace @sync_compatible with @async_dispatch

[desertaxle]

Related to #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

[codspeed-hq]

CodSpeed Performance Report

Merging this PR will not alter performance

_{Comparing add-arun-deployment-async-dispatch (f7e3dba) with main (754ecd5)}

Summary

✅ 2 untouched benchmarks

[zzstoatzz]

sweet!