Upgrade to latest `cargo-dist` version (#13416)

## Summary

Follows https://github.com/astral-sh/uv/pull/7092.

.github/workflows/release.yml

@@ -1,3 +1,5 @@
+# This file was autogenerated by cargo-dist: https://opensource.axo.dev/cargo-dist/
+#
 # Copyright 2022-2024, axodotdev
 # SPDX-License-Identifier: MIT or Apache-2.0
 #
@@ -64,7 +66,7 @@ jobs:
         # we specify bash to get pipefail; it guards against the `curl` command
         # failing. otherwise `sh` won't catch that `curl` returned non-0
         shell: bash
-        run: "curl --proto '=https' --tlsv1.2 -LsSf https://github.com/axodotdev/cargo-dist/releases/download/v0.18.0/cargo-dist-installer.sh | sh"
+        run: "curl --proto '=https' --tlsv1.2 -LsSf https://github.com/axodotdev/cargo-dist/releases/download/v0.22.1/cargo-dist-installer.sh | sh"
       - name: Cache cargo-dist
         uses: actions/upload-artifact@v4
         with:

Cargo.toml

@@ -233,9 +233,9 @@ inherits = "release"
 # Config for 'cargo dist'
 [workspace.metadata.dist]
 # The preferred cargo-dist version to use in CI (Cargo.toml SemVer syntax)
-cargo-dist-version = "0.18.0"
+cargo-dist-version = "0.22.1"
 # CI backends to support
-ci = ["github"]
+ci = "github"
 # The installers to generate for each app
 installers = ["shell", "powershell"]
 # The archive format to use for windows builds (defaults .zip)
@@ -266,11 +266,11 @@ targets = [
 auto-includes = false
 # Whether cargo-dist should create a GitHub Release or use an existing draft
 create-release = true
-# Publish jobs to run in CI
+# Which actions to run on pull requests
 pr-run-mode = "skip"
 # Whether CI should trigger releases with dispatches instead of tag pushes
 dispatch-releases = true
-# The stage during which the GitHub Release should be created
+# Which phase cargo-dist should use to create the GitHub release
 github-release = "announce"
 # Whether CI should include auto-generated code to build local artifacts
 build-local-artifacts = false
@@ -278,9 +278,11 @@ build-local-artifacts = false
 local-artifacts-jobs = ["./build-binaries", "./build-docker"]
 # Publish jobs to run in CI
 publish-jobs = ["./publish-pypi", "./publish-wasm"]
-# Announcement jobs to run in CI
+# Post-announce jobs to run in CI
 post-announce-jobs = ["./notify-dependents", "./publish-docs", "./publish-playground"]
 # Custom permissions for GitHub Jobs
 github-custom-job-permissions = { "build-docker" = { packages = "write", contents = "read" }, "publish-wasm" = { contents = "read", id-token = "write", packages = "write" } }
 # Whether to install an updater program
 install-updater = false
+# Path that installers should place binaries in
+install-path = "CARGO_HOME"