remote_server: Avoid kill for server liveness checks

[Bbrizly]

Objective

check_server_running currently uses kill -0 <pid> to check whether the remote server is still alive.

That works on Unix, but kill is not available on native Windows hosts, so this check is not cross-platform.

This is related to: #55292 Windows SSH remote-server work.

Solution

Use the existing sysinfo process lookup instead of spawning kill.

The same process lookup was already used elsewhere in server.rs, so this also avoids having two different ways of checking whether a PID exists.

Testing

Added a test that verifies the process lookup detects the current process.

• cargo fmt --all -- --check
• cargo test -p remote_server process_exists_finds_current_process
• cargo clippy -p remote_server --all-targets -- -D warnings

Self-Review Checklist:

• I've reviewed my own diff for quality, security, and reliability
• Unsafe blocks (if any) have justifying comments
• The content adheres to Zed's UI standards
• Tests cover the new/changed behavior
• Performance impact has been considered and is acceptable

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Release Notes:

• Fixed remote server liveness checks on Windows hosts.

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[Bbrizly]

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