Default installation fails on `ARC` managed runners

Description:
A default usage of The Github/Microsoft setup-dotnet action on a Github Runner managed by the GitHub/Microsoft actions-runner-controller fails to install.

Task version:

v3

Platform:

• Ubuntu
• macOS
• Windows

Runner type:

• Hosted
• Self-hosted

Repro steps:

name: "Test dotnet"

on:
  workflow_dispatch:
  
jobs:
  "test-aws-secure-access":
    name: "install dot net"
    runs-on: MyOrg-Enterprise-Testing
    steps:
    - uses: actions/setup-dotnet@v3
      with:
        dotnet-version: '3.1.x'

Expected behavior:
The setup-dotnet should install into an unpriviledges path similar to setup-node, setup-python, setup-java. These actions all work out of the box on the Github/Microsoft Actions Runner Controller.

Actual behavior:

Run actions/setup-dotnet@v3
/runner/_work/_actions/actions/setup-dotnet/v3/externals/install-dotnet.sh --channel 3.1
dotnet-install: Note that the intended use of this script is for Continuous Integration (CI) scenarios, where:
dotnet-install: - The SDK needs to be installed without user interaction and without admin rights.
dotnet-install: - The SDK installation doesn't need to persist across multiple CI runs.
dotnet-install: To set up a development environment or to run apps, use installers rather than this script. Visit https://dotnet.microsoft.com/download to get the installer.

mkdir: cannot create directory '/usr/share/dotnet': Permission denied
Error: Failed to install dotnet 1. dotnet-install: Note that the intended use of this script is for Continuous Integration (CI) scenarios, where:

Reproduce the Ubuntu self-hosted workflow using actions/setup-dotnet@v3 on an actions-runner-controller-managed runner. Start with the external install-dotnet.sh invocation shown in the log and compare its install path with the unprivileged behavior expected from the other setup actions. Done means the provided workflow installs .NET without admin rights and no longer fails creating /usr/share/dotnet.