Dependencies not found despite installed on esp-idf framework

### The problem

I was trying to use the IRremoteESP8266 library to implement control of a daikin air conditioner. Code of which can be found [here](https://github.com/SodaWithoutSparkles/esphome-daikin64). The issue is that, when using the esp-idf framework, esphome reports missing dependency, despite installing it.

### Which version of ESPHome has the issue?

2024.4.1 and 2024.4.2

### What type of installation are you using?

Docker

### Which version of Home Assistant has the issue?

Does not matter

### What platform are you using?

ESP32

### Board

Compile time issue, not even installed to hardware

### Component causing the issue

library manager(?)

### Example YAML snippet

```yaml
esphome:
name: test-esp32
friendly_name: test-esp32
includes:
# Find this file at the linked repo
- include/irdaikin.h
libraries:
- crankyoldgit/IRremoteESP8266@^2.8.6

esp32:
board: esp32dev
framework:
# Change this to arduino and it would be fine
type: esp-idf

# Enable logging
logger:

# Enable Home Assistant API
api:
encryption:
key: "REDACTED"

ota:
password: "REDACTED"

wifi:
ssid: !secret wifi_ssid
password: !secret wifi_password

time:
- platform: homeassistant
timezone: Europe/London
id: esptime

switch:
- platform: template
name: "AC status"
id: ac_status
restore_mode: RESTORE_DEFAULT_OFF
optimistic: True

sensor:
- platform: homeassistant
id: living_room_temperature
entity_id: sensor.living_room_temperature
internal: true
climate:
- platform: custom
lambda: |-
auto daikinac = new DaikinAC();
daikinac->set_sensor(id(living_room_temperature));
App.register_component(daikinac);
return {daikinac};
climates:
- name: "AC"
on_state:
- lambda: |-
id(ac_status).publish_state(x.mode != CLIMATE_MODE_OFF);
```

### Anything in the logs that might be useful for us?

```txt
INFO ESPHome 2024.4.1
INFO Reading configuration /config/test-esp32.yaml...
INFO Generating C++ source...
INFO Compiling app...
Processing test-esp32 (board: esp32dev; framework: espidf; platform: platformio/espressif32@5.4.0)
--------------------------------------------------------------------------------
Library Manager: Installing crankyoldgit/IRremoteESP8266 @ ^2.8.6
INFO Installing crankyoldgit/IRremoteESP8266 @ ^2.8.6
Unpacking [####################################] 100%
Library Manager: IRremoteESP8266@2.8.6 has been installed!
INFO IRremoteESP8266@2.8.6 has been installed!
Library Manager: Installing esphome/noise-c @ 0.1.4
INFO Installing esphome/noise-c @ 0.1.4
Unpacking [####################################] 100%
Library Manager: noise-c@0.1.4 has been installed!
INFO noise-c@0.1.4 has been installed!
Library Manager: Resolving dependencies...
INFO Resolving dependencies...
Library Manager: Installing esphome/libsodium @ 1.10018.1
INFO Installing esphome/libsodium @ 1.10018.1
Unpacking [####################################] 100%
Library Manager: libsodium@1.10018.1 has been installed!
INFO libsodium@1.10018.1 has been installed!
HARDWARE: ESP32 240MHz, 320KB RAM, 4MB Flash
- framework-espidf @ 3.40406.240122 (4.4.6)
- tool-cmake @ 3.16.4
- tool-ninja @ 1.7.1
- toolchain-esp32ulp @ 2.35.0-20220830
- toolchain-xtensa-esp32 @ 8.4.0+2021r2-patch5
Reading CMake configuration...
Generating assembly for certificate bundle...
Dependency Graph
|-- noise-c @ 0.1.4
Compiling .pioenvs/test-esp32/src/esphome/components/api/api_connection.o
Compiling .pioenvs/test-esp32/src/esphome/components/api/api_frame_helper.o
Compiling .pioenvs/test-esp32/src/esphome/components/api/api_pb2.o
Compiling .pioenvs/test-esp32/src/esphome/components/api/api_pb2_service.o
Compiling .pioenvs/test-esp32/src/esphome/components/api/api_server.o
Compiling .pioenvs/test-esp32/src/esphome/components/api/list_entities.o
Compiling .pioenvs/test-esp32/src/esphome/components/api/proto.o
Compiling .pioenvs/test-esp32/src/esphome/components/api/subscribe_state.o
Compiling .pioenvs/test-esp32/src/esphome/components/api/user_services.o
Compiling .pioenvs/test-esp32/src/esphome/components/climate/climate.o
Compiling .pioenvs/test-esp32/src/esphome/components/climate/climate_mode.o
Compiling .pioenvs/test-esp32/src/esphome/components/climate/climate_traits.o
Compiling .pioenvs/test-esp32/src/esphome/components/esp32/core.o
Compiling .pioenvs/test-esp32/src/esphome/components/esp32/gpio.o
Compiling .pioenvs/test-esp32/src/esphome/components/esp32/preferences.o
Compiling .pioenvs/test-esp32/src/esphome/components/homeassistant/sensor/homeassistant_sensor.o
Compiling .pioenvs/test-esp32/src/esphome/components/homeassistant/time/homeassistant_time.o
Compiling .pioenvs/test-esp32/src/esphome/components/logger/logger.o
Compiling .pioenvs/test-esp32/src/esphome/components/logger/logger_esp32.o
Compiling .pioenvs/test-esp32/src/esphome/components/logger/logger_esp8266.o
Compiling .pioenvs/test-esp32/src/esphome/components/logger/logger_host.o
Compiling .pioenvs/test-esp32/src/esphome/components/logger/logger_libretiny.o
Compiling .pioenvs/test-esp32/src/esphome/components/logger/logger_rp2040.o
Compiling .pioenvs/test-esp32/src/esphome/components/md5/md5.o
Compiling .pioenvs/test-esp32/src/esphome/components/mdns/mdns_component.o
Compiling .pioenvs/test-esp32/src/esphome/components/mdns/mdns_esp32.o
Compiling .pioenvs/test-esp32/src/esphome/components/mdns/mdns_esp8266.o
Compiling .pioenvs/test-esp32/src/esphome/components/mdns/mdns_host.o
Compiling .pioenvs/test-esp32/src/esphome/components/mdns/mdns_libretiny.o
Compiling .pioenvs/test-esp32/src/esphome/components/mdns/mdns_rp2040.o
Compiling .pioenvs/test-esp32/src/esphome/components/network/util.o
Compiling .pioenvs/test-esp32/src/esphome/components/ota/ota_backend_arduino_esp32.o
Compiling .pioenvs/test-esp32/src/esphome/components/ota/ota_backend_arduino_esp8266.o
Compiling .pioenvs/test-esp32/src/esphome/components/ota/ota_backend_arduino_libretiny.o
Compiling .pioenvs/test-esp32/src/esphome/components/ota/ota_backend_arduino_rp2040.o
Compiling .pioenvs/test-esp32/src/esphome/components/ota/ota_backend_esp_idf.o
Compiling .pioenvs/test-esp32/src/esphome/components/ota/ota_component.o
Compiling .pioenvs/test-esp32/src/esphome/components/sensor/automation.o
Compiling .pioenvs/test-esp32/src/esphome/components/sensor/filter.o
Compiling .pioenvs/test-esp32/src/esphome/components/sensor/sensor.o
Compiling .pioenvs/test-esp32/src/esphome/components/socket/bsd_sockets_impl.o
Compiling .pioenvs/test-esp32/src/esphome/components/socket/lwip_raw_tcp_impl.o
Compiling .pioenvs/test-esp32/src/esphome/components/socket/lwip_sockets_impl.o
Compiling .pioenvs/test-esp32/src/esphome/components/socket/socket.o
Compiling .pioenvs/test-esp32/src/esphome/components/switch/automation.o
Compiling .pioenvs/test-esp32/src/esphome/components/switch/switch.o
Compiling .pioenvs/test-esp32/src/esphome/components/template/switch/template_switch.o
Compiling .pioenvs/test-esp32/src/esphome/components/time/automation.o
Compiling .pioenvs/test-esp32/src/esphome/components/time/real_time_clock.o
Compiling .pioenvs/test-esp32/src/esphome/components/wifi/wifi_component.o
Compiling .pioenvs/test-esp32/src/esphome/components/wifi/wifi_component_esp32_arduino.o
Compiling .pioenvs/test-esp32/src/esphome/components/wifi/wifi_component_esp8266.o
Compiling .pioenvs/test-esp32/src/esphome/components/wifi/wifi_component_esp_idf.o
Compiling .pioenvs/test-esp32/src/esphome/components/wifi/wifi_component_libretiny.o
Compiling .pioenvs/test-esp32/src/esphome/components/wifi/wifi_component_pico_w.o
Compiling .pioenvs/test-esp32/src/esphome/core/application.o
Compiling .pioenvs/test-esp32/src/esphome/core/color.o
Compiling .pioenvs/test-esp32/src/esphome/core/component.o
Compiling .pioenvs/test-esp32/src/esphome/core/component_iterator.o
Compiling .pioenvs/test-esp32/src/esphome/core/controller.o
Compiling .pioenvs/test-esp32/src/esphome/core/entity_base.o
Compiling .pioenvs/test-esp32/src/esphome/core/helpers.o
Compiling .pioenvs/test-esp32/src/esphome/core/log.o
Compiling .pioenvs/test-esp32/src/esphome/core/ring_buffer.o
Compiling .pioenvs/test-esp32/src/esphome/core/scheduler.o
Compiling .pioenvs/test-esp32/src/esphome/core/string_ref.o
Compiling .pioenvs/test-esp32/src/esphome/core/time.o
Compiling .pioenvs/test-esp32/src/esphome/core/util.o
Compiling .pioenvs/test-esp32/src/main.o
Generating LD script .pioenvs/test-esp32/memory.ld
In file included from src/main.cpp:26:
src/irdaikin.h:2:10: fatal error: IRremoteESP8266.h: No such file or directory

*************************************************************************
* Looking for IRremoteESP8266.h dependency? Check our library registry!
*
* CLI > platformio lib search "header:IRremoteESP8266.h"
* Web > https://registry.platformio.org/search?q=header:IRremoteESP8266.h
*
*************************************************************************

#include "IRremoteESP8266.h"
^~~~~~~~~~~~~~~~~~~
compilation terminated.
*** [.pioenvs/test-esp32/src/main.o] Error 1
Compiling .pioenvs/test-esp32/app_trace/app_trace.o
========================= [FAILED] Took 50.62 seconds =========================
```

### Additional information

- https://github.com/SodaWithoutSparkles/esphome-daikin64
- https://github.com/SodaWithoutSparkles/esphome-daikin64/blob/main/irdaikin.h
- https://github.com/esphome/feature-requests/issues/2670
- https://github.com/esphome/feature-requests/issues/1054#issuecomment-765096913
- https://github.com/esphome/feature-requests/issues/444#issuecomment-548166019