Add the Model Context Protocol integration (#135058)

* Add the Model Context Protocol integration

* Improvements to mcp integration

* Move the API prompt constant

* Update config flow error handling

* Update test descriptions

* Update tests/components/mcp/test_config_flow.py

Co-authored-by: Joost Lekkerkerker <joostlek@outlook.com>

* Update tests/components/mcp/test_config_flow.py

Co-authored-by: Joost Lekkerkerker <joostlek@outlook.com>

* Address PR feedback

* Update homeassistant/components/mcp/coordinator.py

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

* Move tool parsing to the coordinator

* Update session handling not to use a context manager

---------

Co-authored-by: Joost Lekkerkerker <joostlek@outlook.com>
Co-authored-by: Paulus Schoutsen <paulus@home-assistant.io>

homeassistant/generated/config_flows.py

@@ -358,6 +358,7 @@ FLOWS = {
         "mailgun",
         "mastodon",
         "matter",
+        "mcp",
         "mcp_server",
         "mealie",
         "meater",