failed to set permissions on `rustup self update`

Verification

• I searched for recent similar issues at https://github.com/rust-lang/rustup/issues?q=is%3Aissue and found no duplicates.
• I am on the latest version of Rustup according to https://github.com/rust-lang/rustup/tags and am still able to reproduce my issue.

Problem

I wanted to try out the new dev version, but the older version failed self-update:

$ RUSTUP_UPDATE_ROOT=https://dev-static.rust-lang.org/rustup rustup update
info: syncing channel updates for 'stable-aarch64-apple-darwin'
info: syncing channel updates for 'nightly-aarch64-apple-darwin'
info: checking for self-update
info: downloading self-update
error: failed to set permissions for '/Users/me/.cargo/bin/rustup-init'

Caused by:
    No such file or directory (os error 2)

$ RUSTUP_UPDATE_ROOT=https://dev-static.rust-lang.org/rustup rustup --version
rustup 1.28.2 (77863418e 2025-04-13)

I have ~/.cargo/bin/rustup, but not rustup-init.

Steps

RUSTUP_UPDATE_ROOT=https://dev-static.rust-lang.org/rustup rustup update

Rustup version

rustup 1.28.2 (77863418e 2025-04-13)

Installed toolchains

Default host: aarch64-apple-darwin
rustup home:  /Users/me/.rustup

installed toolchains
--------------------
stable-aarch64-apple-darwin
nightly-aarch64-apple-darwin (active, default)
nightly-2023-06-14-aarch64-apple-darwin
nightly-2024-06-24-aarch64-apple-darwin
nightly-2025-02-06-aarch64-apple-darwin
1.68.0-aarch64-apple-darwin
1.70.0-aarch64-apple-darwin
1.71.0-aarch64-apple-darwin
1.73.0-aarch64-apple-darwin
1.75.0-aarch64-apple-darwin
1.76.0-aarch64-apple-darwin
1.77.0-aarch64-apple-darwin
1.83.0-aarch64-apple-darwin
stage1
stage2
stage3

active toolchain
----------------
name: nightly-aarch64-apple-darwin
active because: it's the default toolchain
installed targets:
  aarch64-apple-darwin
  aarch64-apple-ios
  thumbv7em-none-eabihf
  wasm32-unknown-unknown
  x86_64-apple-darwin
  x86_64-unknown-linux-musl

OS version

macOS 15.7.3 (24G419)

Start by reproducing the reported command with RUSTUP_UPDATE_ROOT set to the development URL, then trace the self-update path that sets permissions on ~/.cargo/bin/rustup-init. Compare the expected installed files with the reported state, and verify that self-update completes without the missing-file error.