"You must install .NET to run this application"

### Description

all the other issues realted to this error message are either closed, or contain irrelevant information.

this is a trivial repro case that shows that the scripted dotnet sdk install is fundamentally broken.

### Reproduction Steps

run a rocky9 docker container:

```
docker run -it rockylinux:9 /bin/bash
```

in the container's bash prompt, run the following commands:
```
dnf install -qy libicu # required library
curl -s https://dotnet.microsoft.com/download/dotnet/scripts/v1/dotnet-install.sh | bash # install dotnet sdk
export PATH=$PATH:$HOME/.dotnet:$HOME/.dotnet/tools # add dotnet and tools to path
dotnet --info
dotnet tool install --global dotnet-outdated-tool # install a tool
dotnet tool list --global # demonstrate that it's installed correctly
dotnet-outdated # attempt to run it
```

this will install the latest dotnet SDK, install a command (`dotnet-outdated-tool`), and attempt to run it.

the entire output is:

```
Importing GPG key 0x350D275D:
Userid : "Rocky Enterprise Software Foundation - Release key 2022 "
Fingerprint: 21CB 256A E16F C54C 6E65 2949 702D 426D 350D 275D
From : /etc/pki/rpm-gpg/RPM-GPG-KEY-Rocky-9

Installed:
libicu-67.1-9.el9.x86_64

dotnet-install: Attempting to download using aka.ms link https://dotnetcli.azureedge.net/dotnet/Sdk/8.0.401/dotnet-sdk-8.0.401-linux-x64.tar.gz
dotnet-install: Remote file https://dotnetcli.azureedge.net/dotnet/Sdk/8.0.401/dotnet-sdk-8.0.401-linux-x64.tar.gz size is 211866896 bytes.
dotnet-install: Extracting archive from https://dotnetcli.azureedge.net/dotnet/Sdk/8.0.401/dotnet-sdk-8.0.401-linux-x64.tar.gz
dotnet-install: Downloaded file size is 211866896 bytes.
dotnet-install: The remote and local file sizes are equal.
dotnet-install: Installed version is 8.0.401
dotnet-install: Adding to current process PATH: `/root/.dotnet`. Note: This change will be visible only when sourcing script.
dotnet-install: Note that the script does not resolve dependencies during installation.
dotnet-install: To check the list of dependencies, go to https://learn.microsoft.com/dotnet/core/install, select your operating system and check the "Dependencies" section.
dotnet-install: Installation finished successfully.
.NET SDK:
Version: 8.0.401
Commit: 811edcc344
Workload version: 8.0.400-manifests.b6724b7a
MSBuild version: 17.11.4+37eb419ad

Runtime Environment:
OS Name: rocky
OS Version: 9.3
OS Platform: Linux
RID: linux-x64
Base Path: /root/.dotnet/sdk/8.0.401/

.NET workloads installed:
Configured to use loose manifests when installing new manifests.
There are no installed workloads to display.

Host:
Version: 8.0.8
Architecture: x64
Commit: 08338fcaa5

.NET SDKs installed:
8.0.401 [/root/.dotnet/sdk]

.NET runtimes installed:
Microsoft.AspNetCore.App 8.0.8 [/root/.dotnet/shared/Microsoft.AspNetCore.App]
Microsoft.NETCore.App 8.0.8 [/root/.dotnet/shared/Microsoft.NETCore.App]

Other architectures found:
None

Environment variables:
Not set

global.json file:
Not found

Learn more:
https://aka.ms/dotnet/info

Download .NET:
https://aka.ms/dotnet/download

Welcome to .NET 8.0!
---------------------
SDK Version: 8.0.401

Telemetry
---------
The .NET tools collect usage data in order to help us improve your experience. It is collected by Microsoft and shared with the community. You can opt-out of telemetry by setting the DOTNET_CLI_TELEMETRY_OPTOUT environment variable to '1' or 'true' using your favorite shell.

Read more about .NET CLI Tools telemetry: https://aka.ms/dotnet-cli-telemetry

----------------
Installed an ASP.NET Core HTTPS development certificate.
To trust the certificate, view the instructions: https://aka.ms/dotnet-https-linux

----------------
Write your first app: https://aka.ms/dotnet-hello-world
Find out what's new: https://aka.ms/dotnet-whats-new
Explore documentation: https://aka.ms/dotnet-docs
Report issues and find source on GitHub: https://github.com/dotnet/core
Use 'dotnet --help' to see available commands or visit: https://aka.ms/dotnet-cli
--------------------------------------------------------------------------------------
You can invoke the tool using the following command: dotnet-outdated
Tool 'dotnet-outdated-tool' (version '4.6.4') was successfully installed.
Package Id Version Commands
------------------------------------------------------
dotnet-outdated-tool 4.6.4 dotnet-outdated
You must install .NET to run this application.

App: /root/.dotnet/tools/dotnet-outdated
Architecture: x64
App host version: 8.0.8
.NET location: Not found

Learn more:
https://aka.ms/dotnet/app-launch-failed

Download the .NET runtime:
https://aka.ms/dotnet-core-applaunch?missing_runtime=true&arch=x64&rid=linux-x64&os=rocky.9&apphost_version=8.0.8
```

### Expected behavior

sdk is functional after install

### Actual behavior

"You must install .NET to run this application"

### Regression?

_No response_

### Known Workarounds

_No response_

### Configuration

_No response_

### Other information

_No response_