refactor(gateway): extract GatewayTurnExecMixin from run.py (slice 29 of #54962)

[andrexibiza]

Related #54962 #55138

What

Third wave of the GatewayRunner mixin decomposition (gate 4 of #54962): extract the turn-execution engine — 21 methods / ~2,935 lines — out of GatewayRunner in gateway/run.py into a new gateway/turn_exec_mixin.py (GatewayTurnExecMixin), following the codebase's existing mixin pattern (gateway/authz_mixin.py, gateway/kanban_watchers.py, gateway/slash_commands.py).

The mixin holds: the agent run entry points (_run_agent, _run_agent_inner), the remote-proxy path (_get_proxy_url, _build_stream_consumer_config, _run_agent_via_proxy), background-task execution (_run_background_task[_inner]), the cached-agent lifecycle (_init_cached_agent_for_turn, _refresh_agent_cache_message_count, _commit_memory_before_soft_evict, _commit_then_release_soft, _release_evicted_agent_soft, _enforce_agent_cache_cap, _sweep_idle_cached_agents), agent resource cleanup (_should_emit_long_running_notification, _defer_agent_cleanup_until_future_done, _cleanup_agent_resources_off_loop, _cleanup_agent_resources), and the gateway-owned executor (_run_in_executor_with_context, _get_executor, _shutdown_executor).

GatewayRunner now reads class GatewayRunner(GatewayTurnExecMixin, GatewayAuthorizationMixin, GatewayKanbanWatchersMixin, GatewaySlashCommandsMixin) — the new mixin is first in the bases; every self.* call site resolves unchanged via the MRO.

Why

gateway/run.py is a ~26.8k-line god file; the campaign (#54962) decomposes it into focused mixins/modules. This slice is behavior-neutral: every method is lifted verbatim. run.py shrinks from 26,824 to 23,855 lines (−2,969).

How this stays behavior-neutral

• Verbatim moves: 21/21 method bodies identical to the pre-splice run.py (verified by an automated compare against HEAD~2). 14 lines that carried pre-existing trailing whitespace from run.py were whitespace-normalized in the new file (follow-up style commit) so the added file passes git diff --check; run.py's own pre-existing trailing whitespace is untouched. git diff --check over the whole PR diff is clean.
• MRO: no call-site changes; self._x dispatch is unchanged.
• Lazy imports for run.py globals: the moved bodies read a handful of run.py module-level names at call time (_load_gateway_config, _hermes_home, _resolve_gateway_model, _profile_runtime_scope, _platform_config_key, the _AGENT_*/_GATEWAY_* constants, TurnRunner, ...). Each such method gets a deferred from gateway.run import ... at the top of its body (the established pattern in gateway/slash_commands.py) — it resolves at call time when gateway.run is fully loaded, preserving monkeypatch semantics (gateway.run._hermes_home patches in 20+ test files keep working). time is lazy-imported the same way because tests replace gateway.run.time wholesale.
• Logger: module-level logger = logging.getLogger("gateway.run") (same as the kanban/slash mixins) keeps log-record names unchanged.
• No module-level from gateway.run import — no import cycle; the mixin imports only stdlib + direct deps at module top.

How to test

python -m pytest tests/gateway/test_agent_cache.py tests/gateway/test_proxy_mode.py \
  tests/gateway/test_background_command.py tests/gateway/test_53175_cleanup_off_loop.py \
  tests/gateway/test_73297_memory_flush_on_reset.py tests/gateway/test_35994_reset_button_deadlock.py \
  tests/gateway/test_shutdown_cache_cleanup.py tests/gateway/test_multiplex_background_task_scope.py \
  tests/gateway/test_run_cleanup_progress.py tests/gateway/test_turn_context.py \
  tests/gateway/test_incomplete_gateway_turns.py tests/gateway/test_tool_log_mode.py \
  tests/gateway/test_7100_transient_failure_transcript.py tests/gateway/test_stale_finalize_suppression.py \
  tests/gateway/test_transcript_offset.py tests/gateway/test_42039_duplicate_user_message.py \
  tests/gateway/test_session_id_cache_coherence.py tests/gateway/test_shutdown_memory_provider_messages.py \
  -q --no-header -p no:cacheprovider

Import smoke: import gateway.run; assert hasattr(gateway.run.GatewayRunner, '_run_agent_inner') and all 21 moved methods report __module__ == 'gateway.turn_exec_mixin' with GatewayTurnExecMixin first in GatewayRunner.__mro__.

Platforms tested

• Windows 10 (git-bash), Python 3.11 (repo venv). Targeted suites: 174 tests across 29 files, all green (95 core batch: agent cache, proxy mode, background command, cleanup, turn context, tool log mode, transcript/incomplete-turn paths, session-id coherence; 79 follow-up batch: executor/run-progress, startup/shutdown, TTS gateway, fallback-chain reload, auto-continue), plus 62 re-run green on the final committed state (post whitespace-fix).
• scripts/check-windows-footguns.py on the new module: clean.

Scope note

• Only the 21 listed methods move; everything else in GatewayRunner stays. Two class-level section comments that described the moved proxy cluster travel with it; the _CLEANUP_TIMEOUT_S class attribute stays on GatewayRunner (still referenced via self by the moved cleanup methods through the MRO).
• The moved methods keep their in-function imports verbatim (e.g. from run_agent import AIAgent); no run.py imports were pruned (other methods may still use them).
• One source-level test (tests/gateway/test_fallback_chain_reload.py) pins the location of the two fallback_model=self._refresh_fallback_model() agent-construction sites; both sites moved into the mixin, so the test now counts across gateway/run.py + gateway/turn_exec_mixin.py (same invariant, same pattern as the TurnRunner extraction commit 1a3a9de).

Part of #54962
Part of #55138

Part of #78207
Part of #78647
Part of #78791