SSH tries to use default private key even if use_password is specified

Bug Report

Issue name

SSH tries to use default private key even if use_password is specified

Description

.dvc/config:

['core']
    remote = myserver

['remote "myserver"']
    url = ssh://myuser@mypublicip:/data
    ask_password = true

~/.ssh/config :

Nothing related to mypublicip.

When I run uv run dvc push:

$ uv run dvc push
Collecting                                                                                                                                                                                                                      |1.00 [00:00,  118entry/s]
PushingEnter a password for myuser@myserver:
# (I enter password here)
                                                                                                                                                                                                                                                         Enter passphrase for key '~/.ssh/id_ed25519': ent/files/md5'|                                                                                                                                                         |0/? [00:00<?,    ?files/s]
Enter passphrase for key '~/.ssh/id_ed25519': 
Enter passphrase for key '~/.ssh/id_ed25519': 
Pushing
Everything is up to date.  

You can see that I just press Enter when it tries to decrypt my private key, then gives up, but it works anyway because of course, the password I previously entered authenticates myuser and '~/.ssh/id_ed25519' has nothing to do with the host...

Reproduce

See above.

Expected

Asks for password to authenticate as myuser and doesn't ask me to unlock my default ssh key that doesn't even authenticate to mypublicip and is not listed in ~/.ssh/config

Environment information

I am using uv for my virtual env with the following pyproject.toml:

[project]
name = "project-name"
version = "0"
requires-python = ">=3.14"

dependencies = [
  "dvc[ssh]",
]

Output of dvc doctor:

DVC version: 3.63.0 (pip)
-------------------------
Platform: Python 3.14.0 on Linux-6.6.87.2-microsoft-standard-WSL2-x86_64-with-glibc2.39
Subprojects:
        dvc_data = 3.16.12
        dvc_objects = 5.1.2
        dvc_render = 1.0.2
        dvc_task = 0.40.2
        scmrepo = 3.5.3
Supports:
        http (aiohttp = 3.13.2, aiohttp-retry = 2.9.1),
        https (aiohttp = 3.13.2, aiohttp-retry = 2.9.1),
        ssh (sshfs = 2025.10.0)
Config:
        Global: ~/.config/dvc
        System: /etc/xdg/dvc
Cache types: hardlink, symlink
Cache directory: ext4 on /dev/sdd
Caches: local
Remotes: ssh
Workspace directory: ext4 on /dev/sdd
Repo: dvc, git
Repo.site_cache_dir: /var/tmp/dvc/repo/2546558791564caae91c6453b68d4f38

Reproduce the prompt sequence with uv run dvc push using the shown .dvc/config and empty ~/.ssh/config; inspect the SSH remote path and the reported sshfs support version. Trace where password authentication and the default private-key prompt are selected. Done means password authentication no longer prompts to unlock the unrelated default key, while the push still succeeds.