Add the Model Context Protocol Server integration (#134122)

* Add the Model Context Protocol Server integration

* Remove unusued code in init

* Fix comment wording

* Use util.uild for unique ids

* Set config entry title to the LLM API name

* Extract an SSE parser and update comments

* Update comments and defend against already closed sessions

* Shorten description

* Update homeassistant/components/mcp_server/__init__.py

Co-authored-by: Paulus Schoutsen <paulus@home-assistant.io>

* Change integration type to service

---------

Co-authored-by: Paulus Schoutsen <paulus@home-assistant.io>

homeassistant/generated/config_flows.py

@@ -356,6 +356,7 @@ FLOWS = {
         "mailgun",
         "mastodon",
         "matter",
+        "mcp_server",
         "mealie",
         "meater",
         "medcom_ble",

homeassistant/generated/integrations.json

@@ -3590,6 +3590,13 @@
       "config_flow": true,
       "iot_class": "local_push"
     },
+    "mcp_server": {
+      "name": "Model Context Protocol Server",
+      "integration_type": "service",
+      "config_flow": true,
+      "iot_class": "local_push",
+      "single_config_entry": true
+    },
     "mealie": {
       "name": "Mealie",
       "integration_type": "service",