Fix default NuGet packages restore folder

[eerhardt]

We shouldn't default to ~/.nuget/packages. Instead we should use NuGet defaulting logic.

Refactor the restore code using the patterns from the NuGet.Client sources. This simplifies the code.

Fix #15404

[github-actions]

🚀 Dogfood this PR with:

⚠️ WARNING: Do not do this without first carefully reviewing the code of this PR to satisfy yourself it is safe.

curl -fsSL https://raw.githubusercontent.com/microsoft/aspire/main/eng/scripts/get-aspire-cli-pr.sh | bash -s -- 15416

Or

• Run remotely in PowerShell:

iex "& { $(irm https://raw.githubusercontent.com/microsoft/aspire/main/eng/scripts/get-aspire-cli-pr.ps1) } 15416"

[eerhardt]

/backport to release/13.2

[github-actions]

Started backporting to release/13.2: https://github.com/dotnet/aspire/actions/runs/23323572778

[Copilot]

Pull request overview

Updates RestoreCommand to use NuGet’s built-in settings resolution for the global packages folder instead of hard-coding ~/.nuget/packages, aligning behavior with NuGet defaults and config.

Changes:

• Replace hard-coded user-profile-based packages folder with NuGet settings-based resolution.
• Load NuGet configuration settings and compute the global packages folder via SettingsUtility.

[github-actions]

Re-running the failed jobs in the CI workflow for this pull request because 3 jobs were identified as retry-safe transient failures in the CI run attempt.
GitHub was asked to rerun all failed jobs for that attempt, and the rerun is being tracked in the rerun attempt.
The job links below point to the failed attempt jobs that matched the retry-safe transient failure rules.

• Tests / Npgsql / Npgsql (ubuntu-latest) - Failed step 'Build test project' will be retried because the job log shows a likely transient infrastructure network failure. Matched pattern: /Unable to load the service index for source https:\/\/(?:pkgs\.dev\.azure\.com\/dnceng|dnceng\.pkgs\.visualstudio\.com)\/public\/_packaging\//i.
• Tests / Microsoft.EntityFrameworkCore.Cosmos / Microsoft.EntityFrameworkCore.Cosmos (ubuntu-latest) - Failed step 'Build test project' will be retried because the job log shows a likely transient infrastructure network failure. Matched pattern: /Unable to load the service index for source https:\/\/(?:pkgs\.dev\.azure\.com\/dnceng|dnceng\.pkgs\.visualstudio\.com)\/public\/_packaging\//i.
• Tests / Dashboard / Dashboard (ubuntu-latest) - Failed step 'Build test project' will be retried because the job log shows a likely transient infrastructure network failure. Matched pattern: /Unable to load the service index for source https:\/\/(?:pkgs\.dev\.azure\.com\/dnceng|dnceng\.pkgs\.visualstudio\.com)\/public\/_packaging\//i.