refactor(install): decouple helpers from process then re-use the resolution result

src/cli/proxy_mode.rs

@@ -14,7 +14,7 @@ pub async fn main(
     current_dir: PathBuf,
     process: &Process,
 ) -> anyhow::Result<ExitStatus> {
-    self_update::cleanup_self_updater(process)?;
+    self_update::cleanup_self_updater(&process.cargo_home()?.join("bin"))?;
 
     let _setup = job::setup();
     let mut args = process.args_os().skip(1);

src/cli/rustup_mode.rs

@@ -703,7 +703,7 @@ pub async fn main(
         .bin("rustup")
         .complete();
 
-    self_update::cleanup_self_updater(process)?;
+    self_update::cleanup_self_updater(&process.cargo_home()?.join("bin"))?;
 
     use clap::error::ErrorKind::*;
     let matches = match Rustup::try_parse_from(process.args_os()) {