Function resolve_par_term_binary 

pub fn resolve_par_term_binary(
    explicit: Option<&Path>,
) -> Result<PathBuf, Box<dyn Error + Send + Sync>>

Resolve the par-term binary to use for hosting the MCP server.

Resolution order:

1. explicit — if provided, return it immediately (no existence check).
2. Same directory as the current executable — used in bundled/installed layouts.
3. System PATH lookup via resolve_binary_in_path.

Returns an error if none of the above succeed.