### Summary

When using the `copy` module with `become: true` and `remote_src: true` the owner of the destination file is `root` rather than the owner of the source file.

### Issue Type

Feature request/Documentation report

### Component Name

copy

### Ansible Version

```console
$ ansible --version
ansible [core 2.14.3]
  config file = /etc/ansible/ansible.cfg
  configured module search path = ['/home/Laborratte5/.ansible/plugins/modules', '/usr/share/ansible/plugins/modules']
  ansible python module location = /usr/lib/python3.10/site-packages/ansible
  ansible collection location = /home/Laborratte5/.ansible/collections:/usr/share/ansible/collections
  executable location = /usr/bin/ansible
  python version = 3.10.9 (main, Dec 19 2022, 17:35:49) [GCC 12.2.0] (/usr/bin/python)
  jinja version = 3.1.2
  libyaml = True
```


### Configuration

```console
# if using a version older than ansible-core 2.12 you should omit the '-t all'
$ ansible-config dump --only-changed -t all
CONFIG_FILE() = /etc/ansible/ansible.cfg
```


### OS / Environment

Control Node: Arch Linux
Managed Node: Debian GNU/Linux 11 (bullseye)

### Steps to Reproduce

<!--- Paste example playbooks or commands between quotes below -->
```yaml (paste below)
    - name: Copy test
      become: true
      ansible.builtin.copy:
        src: "/home/provision/copytest.src"
        remote_src: true
        dest: "/home/provision/copytest.dest"
        mode: preserve
```


### Expected Results

I expected `copytest.dest` file having owner:group of `provision:provision`.

### Actual Results

```console
-rw-r--r-- 1 root      root      8  5. Mär 00:22 copytest.dest
-rw-r--r-- 1 provision provision 8  5. Mär 00:22 copytest.src

changed: [test_server01] => {
    "changed": true,
    "checksum": "a32ac2d7196b96b084a4e9d792fa8fba7f1ed29d",
    "dest": "/home/provision/copytest.dest",
    "gid": 0,
    "group": "root",
    "md5sum": "4a251a2ef9bbf4ccc35f97aba2c9cbda",
    "mode": "0644",
    "owner": "root",
    "size": 8,
    "src": "/home/provision/copytest.src",
    "state": "file",
    "uid": 0
}
```


### Code of Conduct

- [X] I agree to follow the Ansible Code of Conduct
description:
    - The permissions of the destination file or directory.
    - For those used to C(/usr/bin/chmod) remember that modes are actually octal numbers.
      You must either add a leading zero so that Ansible's YAML parser knows it is an octal number
      (like V(0644) or V(01777)) or quote it (like V('644') or V('1777')) so Ansible receives a string
      and can do its own conversion from string into number. Giving Ansible a number without following
      one of these rules will end up with a decimal number which will have unexpected results.
    - As of Ansible 1.8, the mode may be specified as a symbolic mode (for example, V(u+rwx) or V(u=rw,g=r,o=r)).
    - As of Ansible 2.3, the mode may also be the special string V(preserve).
    - V(preserve) means that the file will be given the same permissions as the source file.
    - When doing a recursive copy, see also O(directory_mode).
    - If O(mode) is not specified and the destination file B(does not) exist, the default C(umask) on the system will be used
      when setting the mode for the newly created file.
    - If O(mode) is not specified and the destination file B(does) exist, the mode of the existing file will be used.
    - Specifying O(mode) is the best way to ensure files are created with the correct permissions.
      See CVE-2020-1736 for further details.
  directory_mode:
    description:
    - Set the access permissions of newly created directories to the given mode.
      Permissions on existing directories do not change.
    - See O(mode) for the syntax of accepted values.
    - The target system's defaults determine permissions when this parameter is not set.
    type: raw
    version_added: '1.5'
  remote_src:
    description:
    - Influence whether O(src) needs to be transferred or already is present remotely.
    - If V(false), it will search for O(src) on the controller node.
    - If V(true) it will search for O(src) on the managed (remote) node.
    - O(remote_src) supports recursive copying as of version 2.8.