[bluetooth_connection] Support 3 connection slots on rp2

tests/component_tests/bluetooth_proxy/config/rp2_proxy_default.yaml

@@ -0,0 +1,15 @@
+esphome:
+  name: poolwrap-rp2-default
+
+rp2:
+  board: rpipicow
+
+wifi:
+  ssid: MySSID
+  password: password1
+
+api:
+
+rp2_ble_tracker:
+
+bluetooth_proxy:

tests/component_tests/bluetooth_proxy/config/rp2_proxy_single_slot.yaml

@@ -0,0 +1,16 @@
+esphome:
+  name: poolwrap-rp2-single
+
+rp2:
+  board: rpipicow
+
+wifi:
+  ssid: MySSID
+  password: password1
+
+api:
+
+rp2_ble_tracker:
+
+bluetooth_proxy:
+  connection_slots: 1

tests/component_tests/bluetooth_proxy/test_platform_gates.py

@@ -139,8 +139,8 @@ def test_rp2_defaults_to_the_full_proxy(
     _register_tracker(PLATFORM_RP2)
     validated = bluetooth_proxy.CONFIG_SCHEMA({})
     assert validated[CONF_ACTIVE] is True
-    assert validated[bluetooth_proxy.CONF_CONNECTION_SLOTS] == 1
-    assert len(validated[bluetooth_proxy.CONF_CONNECTIONS]) == 1
+    assert validated[bluetooth_proxy.CONF_CONNECTION_SLOTS] == 3
+    assert len(validated[bluetooth_proxy.CONF_CONNECTIONS]) == 3
 
 
 def test_rp2_accepts_explicit_passive(
@@ -156,11 +156,15 @@ def test_rp2_accepts_explicit_passive(
 def test_rp2_rejects_slots_beyond_the_btstack_limit(
     set_core_config: SetCoreConfigCallable,
 ) -> None:
-    # The prebuilt BTstack library allows exactly one GATT client connection.
+    # The BTstack pool overrides are sized for RP2_MAX_CONNECTIONS slots.
     set_core_config(PlatformFramework.RP2_ARDUINO)
     _register_tracker(PLATFORM_RP2)
-    with pytest.raises(cv.Invalid, match="at most 1 connection slot"):
-        bluetooth_proxy.CONFIG_SCHEMA({"connection_slots": 2})
+    with pytest.raises(cv.Invalid, match="at most 3 connection slot"):
+        bluetooth_proxy.CONFIG_SCHEMA({"connection_slots": 4})
+    # Fewer slots than the cap stay accepted (the prebuilt single-client pool
+    # path for 1, the wrap path for 2).
+    validated = bluetooth_proxy.CONFIG_SCHEMA({"connection_slots": 1})
+    assert len(validated[bluetooth_proxy.CONF_CONNECTIONS]) == 1
     # Values past even the loosest platform cap stop at the outer walkable
     # schema, which stays bounded for range walkers (device-builder sync);
     # in-range values get the platform message above.

tests/component_tests/bluetooth_proxy/test_rp2_pool_wrap.py

@@ -0,0 +1,37 @@
+"""The rp2 BTstack pool overrides: multi-slot builds emit the --wrap flags
+that swap the prebuilt single-client pools for the codegen-sized ones;
+single-slot builds emit none and stay byte-identical to previous releases."""
+
+from __future__ import annotations
+
+from collections.abc import Callable
+from pathlib import Path
+
+from esphome.components import bluetooth_connection
+from esphome.core import CORE
+
+from ..helpers import get_define_value
+
+WRAP_FLAGS = tuple(
+    f"-Wl,--wrap={symbol}" for symbol in bluetooth_connection._RP2_BTSTACK_POOL_SYMBOLS
+)
+
+
+def test_default_slots_emit_the_pool_wrap(
+    generate_main: Callable[[str | Path], str],
+    component_config_path: Callable[[str], Path],
+) -> None:
+    generate_main(component_config_path("rp2_proxy_default.yaml"))
+    assert all(flag in CORE.build_flags for flag in WRAP_FLAGS)
+    assert get_define_value("ESPHOME_BLE_GATT_CLIENT_COUNT") == "3"
+    assert get_define_value("BLUETOOTH_PROXY_MAX_CONNECTIONS") == "3"
+
+
+def test_single_slot_keeps_the_prebuilt_pools(
+    generate_main: Callable[[str | Path], str],
+    component_config_path: Callable[[str], Path],
+) -> None:
+    generate_main(component_config_path("rp2_proxy_single_slot.yaml"))
+    assert not any(flag in CORE.build_flags for flag in WRAP_FLAGS)
+    assert get_define_value("ESPHOME_BLE_GATT_CLIENT_COUNT") == "1"
+    assert get_define_value("BLUETOOTH_PROXY_MAX_CONNECTIONS") == "1"