[api] Add an integration test for the encode branch boundaries

Covers a zero float that is skipped on the wire, a fixed32 state, a
negative int32, list entity strings and text states whose length
prefix needs two varint bytes, a two byte field tag through the
device info area, and the field free disconnect exchange.

tests/integration/fixtures/api_encode_boundaries.yaml

@@ -0,0 +1,58 @@
+esphome:
+  name: api-encode-boundaries-test
+  # Top-level area fills DeviceInfoResponse.suggested_area (field 16, a two-byte tag)
+  area:
+    id: kitchen_area
+    name: Kitchen
+  on_boot:
+    - sensor.template.publish:
+        id: zero_then_value
+        state: 0.0
+
+host:
+api:
+logger:
+  level: DEBUG
+
+sensor:
+  - platform: template
+    name: "Zero Then Value"
+    id: zero_then_value
+    # Negative int32 takes the ten byte varint path
+    accuracy_decimals: -2
+    update_interval: never
+
+text_sensor:
+  - platform: template
+    name: "Long Text"
+    id: long_text
+    update_interval: never
+
+number:
+  - platform: template
+    name: "Negative Number"
+    optimistic: true
+    min_value: -1000
+    max_value: 1000
+    step: 0.5
+    initial_value: -123.5
+
+select:
+  - platform: template
+    name: "Long Option Select"
+    optimistic: true
+    options:
+      - short
+      - "option-with-a-name-long-enough-that-its-length-prefix-needs-two-varint-bytes-when-the-list-entities-response-is-encoded-xxxxxxxxxx"
+    initial_option: short
+
+button:
+  - platform: template
+    name: "Publish Values"
+    on_press:
+      - sensor.template.publish:
+          id: zero_then_value
+          state: 12.5
+      - text_sensor.template.publish:
+          id: long_text
+          state: !lambda return std::string(200, 'y');

tests/integration/test_api_encode_boundaries.py

@@ -0,0 +1,82 @@
+"""Encode paths at their branch boundaries: zero skipped float, fixed32 state, negative int32,
+length prefixes of two varint bytes, two byte field tags and a clean disconnect."""
+
+from __future__ import annotations
+
+import asyncio
+
+from aioesphomeapi import (
+    EntityState,
+    NumberState,
+    SelectInfo,
+    SensorInfo,
+    SensorState,
+    TextSensorState,
+)
+import pytest
+
+from .state_utils import InitialStateHelper, require_entity
+from .types import APIClientConnectedFactory, RunCompiledFunction
+
+LONG_OPTION = (
+    "option-with-a-name-long-enough-that-its-length-prefix-needs-two-varint-bytes-"
+    "when-the-list-entities-response-is-encoded-xxxxxxxxxx"
+)
+
+
+@pytest.mark.asyncio
+async def test_api_encode_boundaries(
+    yaml_config: str,
+    run_compiled: RunCompiledFunction,
+    api_client_connected: APIClientConnectedFactory,
+) -> None:
+    loop = asyncio.get_running_loop()
+    async with run_compiled(yaml_config), api_client_connected() as client:
+        device_info = await client.device_info()
+        assert device_info.suggested_area == "Kitchen"
+
+        entities, _ = await client.list_entities_services()
+        sensor = require_entity(entities, "zero_then_value", SensorInfo)
+        assert sensor.accuracy_decimals == -2
+        select = require_entity(entities, "long_option_select", SelectInfo)
+        assert len(LONG_OPTION) >= 128
+        assert select.options == ["short", LONG_OPTION]
+        text = require_entity(entities, "long_text")
+        number = require_entity(entities, "negative_number")
+        button = require_entity(entities, "publish_values")
+
+        sensor_value: asyncio.Future[float] = loop.create_future()
+        text_value: asyncio.Future[str] = loop.create_future()
+        initial = InitialStateHelper(entities)
+
+        def on_state(state: EntityState) -> None:
+            if (
+                isinstance(state, SensorState)
+                and state.key == sensor.key
+                and not sensor_value.done()
+            ):
+                sensor_value.set_result(state.state)
+            elif (
+                isinstance(state, TextSensorState)
+                and state.key == text.key
+                and not text_value.done()
+            ):
+                text_value.set_result(state.state)
+
+        client.subscribe_states(initial.on_state_wrapper(on_state))
+        await initial.wait_for_initial_states()
+
+        # A float of exactly zero is skipped on the wire and must still read as 0.0, not missing
+        first = initial.initial_states[sensor.key]
+        assert isinstance(first, SensorState)
+        assert first.state == 0.0 and not first.missing_state
+        first_number = initial.initial_states[number.key]
+        assert isinstance(first_number, NumberState)
+        assert first_number.state == -123.5
+
+        client.button_command(button.key)
+        assert await asyncio.wait_for(sensor_value, 5.0) == 12.5
+        assert await asyncio.wait_for(text_value, 5.0) == "y" * 200
+
+        # DisconnectRequest and DisconnectResponse carry no fields
+        await client.disconnect()