Create bootstrap tasks eagerly (#111497)

We can avoid one event loop iteration to start the tasks here

homeassistant/bootstrap.py

@@ -2,7 +2,6 @@
 from __future__ import annotations
 
 import asyncio
-from collections.abc import Coroutine
 import contextlib
 from datetime import timedelta
 import logging
@@ -51,6 +50,7 @@ from .setup import (
     async_set_domains_to_be_loaded,
     async_setup_component,
 )
+from .util.async_ import create_eager_task
 from .util.logging import async_activate_log_queue_handler
 from .util.package import async_get_user_site, is_virtual_env
 
@@ -667,7 +667,7 @@ async def _async_resolve_domains_to_setup(
             to_get = old_to_resolve
 
         manifest_deps: set[str] = set()
-        resolve_dependencies_tasks: list[Coroutine[Any, Any, bool]] = []
+        resolve_dependencies_tasks: list[asyncio.Task[bool]] = []
         integrations_to_process: list[loader.Integration] = []
 
         for domain, itg in (await loader.async_get_integrations(hass, to_get)).items():
@@ -679,7 +679,13 @@ async def _async_resolve_domains_to_setup(
             manifest_deps.update(itg.after_dependencies)
             needed_requirements.update(itg.requirements)
             if not itg.all_dependencies_resolved:
-                resolve_dependencies_tasks.append(itg.resolve_dependencies())
+                resolve_dependencies_tasks.append(
+                    create_eager_task(
+                        itg.resolve_dependencies(),
+                        name=f"resolve dependencies {domain}",
+                        loop=hass.loop,
+                    )
+                )
 
         if unseen_deps := manifest_deps - integration_cache.keys():
             # If there are dependencies, try to preload all
@@ -712,6 +718,7 @@ async def _async_resolve_domains_to_setup(
     hass.async_create_background_task(
         requirements.async_load_installed_versions(hass, needed_requirements),
         "check installed requirements",
+        eager_start=True,
     )
     # Start loading translations for all integrations we are going to set up
     # in the background so they are ready when we need them. This avoids a
@@ -726,6 +733,7 @@ async def _async_resolve_domains_to_setup(
     hass.async_create_background_task(
         translation.async_load_integrations(hass, {*BASE_PLATFORMS, *domains_to_setup}),
         "load translations",
+        eager_start=True,
     )
 
     return domains_to_setup, integration_cache