GH-48766: [CI][Packaging] Delete conan related packaging jobs and CI (#49647)

### Rationale for this change

The conan CI jobs have been failing for 4+ months. The main problem is that conan deprecated the repository they used to build the Docker files we were using:

>    ⛔ This repository is now deprecated. The Docker recipes and images provided by this repository are no longer used by ConanCenterIndex CI. Users are encouraged to explore alternative solutions for their Docker image needs.

see:
https://github.com/conan-io/conan-docker-tools#readme

### What changes are included in this PR?

Remove all conan related Arrow CI. The integration will have to be managed upstream when we build the PRs to conan. This might required patches and take longer but having the CI jobs broken for 4+ months without a clear guideline on how to proceed should be fixed.

### Are these changes tested?

No

### Are there any user-facing changes?

No
* GitHub Issue: #48766

Authored-by: Raúl Cumplido <raulcumplido@gmail.com>
Signed-off-by: Sutou Kouhei <kou@clear-code.com>

Author: raulcd

.env

@@ -100,9 +100,3 @@ VCPKG="66c0373dc7fca549e5803087b9487edfe3aca0a1"    # 2026.01.16 Release
 # use pulled built images in dev/tasks/python-wheels/github.windows.yml.
 PYTHON_WHEEL_WINDOWS_IMAGE_REVISION=2026-03-04
 PYTHON_WHEEL_WINDOWS_TEST_IMAGE_REVISION=2026-03-04
-
-# Use conanio/${CONAN_BASE}:{CONAN_VERSION} for "docker compose run --rm conan".
-# See https://github.com/conan-io/conan-docker-tools#readme and
-# https://hub.docker.com/u/conanio for available images.
-CONAN_BASE=gcc11-ubuntu16.04
-CONAN_VERSION=2.12.1

.pre-commit-config.yaml

@@ -268,7 +268,6 @@ repos:
           )
         exclude: >-
           (
-          ?^ci/conan/all/.*CMakeLists\.txt$|
           ?^cpp/cmake_modules/FindNumPy\.cmake$|
           ?^cpp/cmake_modules/FindPythonLibsNew\.cmake$|
           ?^cpp/cmake_modules/UseCython\.cmake$|
@@ -299,8 +298,6 @@ repos:
           ?^ci/scripts/c_glib_build\.sh$|
           ?^ci/scripts/c_glib_test\.sh$|
           ?^ci/scripts/ccache_setup\.sh$|
-          ?^ci/scripts/conan_build\.sh$|
-          ?^ci/scripts/conan_setup\.sh$|
           ?^ci/scripts/cpp_test\.sh$|
           ?^ci/scripts/download_tz_database\.sh$|
           ?^ci/scripts/install_azurite\.sh$|

LICENSE.txt

@@ -2087,30 +2087,6 @@ SPDX-License-Identifier: Apache-2.0
 
 --------------------------------------------------------------------------------
 
-ci/conan/ is based on code from Conan Package and Dependency Manager.
-
-Copyright (c) 2019 Conan.io
-
-Permission is hereby granted, free of charge, to any person obtaining a copy
-of this software and associated documentation files (the "Software"), to deal
-in the Software without restriction, including without limitation the rights
-to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-copies of the Software, and to permit persons to whom the Software is
-furnished to do so, subject to the following conditions:
-
-The above copyright notice and this permission notice shall be included in all
-copies or substantial portions of the Software.
-
-THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
-SOFTWARE.
-
---------------------------------------------------------------------------------
-
 3rdparty dependency UCX is redistributed as a dynamically linked shared
 library in certain binary distributions. UCX has the following license: