Clean up iteration residue from the review rounds

- Drop unused includes (ble_client_state.h, <utility>) and the unused
  notify/indicate property constants (no CCCD path yet)
- Note the frozen node-facing surface on the uncalled backend forwarders
- Keep the legacy-only 'name' key out of the neutral schema
- Move the slot-ledger test to tests/component_tests/bluetooth_connection
- Comment accuracy fixes (choke-point wording, wrapped lines, backoff note)

tests/component_tests/bluetooth_connection/test_slot_ledger.py

@@ -0,0 +1,17 @@
+"""Tests for the cross-component GATT slot ledger."""
+
+import pytest
+
+from esphome import config_validation as cv
+from esphome.components import bluetooth_connection
+from esphome.const import KEY_CORE, KEY_TARGET_PLATFORM, PLATFORM_RP2
+from esphome.core import CORE
+
+
+def test_gatt_slot_ledger_rejects_overcommit_on_rp2() -> None:
+    # The cross-component cap must reject two claims on rp2.
+    CORE.data.setdefault(KEY_CORE, {})[KEY_TARGET_PLATFORM] = PLATFORM_RP2
+    bluetooth_connection.consume_gatt_slot("bluetooth_proxy")({})
+    bluetooth_connection.consume_gatt_slot("ble_client")({})
+    with pytest.raises(cv.Invalid, match="supports at most 1 GATT client"):
+        bluetooth_connection.FINAL_VALIDATE_SCHEMA({})