[NETSDKE2E] [Dotnetup]Re-run dotnetup init failed with error The install path already contains a .NET installation that is not tracked by dotnetup after interrupted init

### Prerequisites

- [x] I have read the [dotnetup documentation](https://github.com/dotnet/sdk/tree/release/dnup/documentation/general/dotnetup).
- [x] I have searched for [existing dotnetup issues](https://github.com/dotnet/sdk/issues?q=is%3Aissue%20state%3Aopen%20label%3Adotnetup).
- [x] I have searched for [existing dotnetup discussions](https://github.com/dotnet/sdk/discussions/categories/dotnetup).

### Issue type

Bug report

### Description

INSTALL STEPS

Clean machine: Win11 x64 25h2 ENU
Install dotnetup tool: iwr https://aka.ms/dotnetup/get-dotnetup.ps1 | iex
Add dotnetup to the PATH in Current session.

Repro Steps

1. Open PS terminal, run `dotnetup init ` with default settings, when the .NET SDk is progress of installing, close the PS terminal immediately
2. Open a new PS terminal, re-run `dotnetup init `and observe

Expected Result
`dotnetup init ` works fine.

Actual Result
`dotnetup init ` failed with error The install path already contains a .NET installation that is not tracked by dotnetup

### dotnetup version

0.1.4-preview.6.26358.1+5a6ef780cc88ce7bcafcb3a9c5cfc70da5c3a313

Start by reproducing `dotnetup init` on a clean Windows 11 x64 machine, interrupting the installation and running the command again. Trace the handling of interrupted installations and verify that a rerun completes without reporting an untracked .NET installation.

Written by the indexing model from the issue text.