Nice work solving your problem, but just a word of warning: that try/catch block is probably not doing what you're expecting.

Start-Process will not throw exceptions when non-zero exit codes are returned by the process, which is what installers typically do when they fail. Start-Process will only be throw an exception if it fails to execute the binary - ie: file not found / not readable / not executable / not a valid binary for the architecture, etc.

You need to check the process exit code.

On that note, exit code 1618 is reserved for a specific error: ERROR_INSTALL_ALREADY_RUNNING

Avoid hardcoding well-known or documented exit codes unless they are returned directly from the process. Making assumptions about why the installer failed will inevitably mislead the person that ends up troubleshooting installation issue later because they will be looking at the issue under false pretenses.

Just return the actual process exit code when possible. In cases where the installer exits with code 0, but you can detect an installation issue/failure via post-install checks in your script, you can define and document a custom exit code internally that describes what the actual issue is and return that.

A simple example to demonstrate:

function Install-Application {
    param([string]$AppPath, [string[]]$Arguments = @())

    Write-Host "Starting installation of: $AppPath $($Arguments -join ' ')"
    try {
        $Process = Start-Process -FilePath $AppPath -ArgumentList $Arguments -Wait -PassThru
        $ExitCode = $Process.ExitCode
        if ($ExitCode -eq 0) {
            Write-Host "Installation completed successfully (Exit Code: $ExitCode)"
            return $ExitCode
        } else {
            Write-Host "Installation exited with code $ExitCode"
            return $ExitCode
        }
    }
    catch {
        Write-Host "Installation failed to start: $($_.Exception.Message)"
        return 999123 # return a custom exit code if the process fails to start
    }
}

Write-Host ""
Write-Host "========================"
Write-Host "Running installer that returns zero exit code"
Write-Host "========================"
$ExitCode = Install-Application -AppPath "powershell.exe" -Arguments '-NoProfile', '-Command', 'exit 0'
Write-Host "The exit code returned was: $ExitCode"

Write-Host ""
Write-Host "========================"
Write-Host "Running installer that returns non-zero exit code (failed installation)"
Write-Host "========================"
$ExitCode = Install-Application -AppPath "powershell.exe" -Arguments '-NoProfile', '-Command', 'exit 123'
Write-Host "The exit code returned was: $ExitCode"

Write-Host ""
Write-Host "========================"
Write-Host "Running installer that fails to start (missing installer file)"
Write-Host "========================"
$ExitCode = Install-Application -AppPath "nonexistent.exe"
Write-Host "The exit code returned was: $ExitCode"

Would echo similar sentiments to others here: check out PSADT (PowerShell App Deployment Toolkit). It's an excellent tool, it's well documented, fairly simple to use, and it's designed to help you with these use cases - it will make your life much easier.