[WebToolsE2E][Aspire] When using the 'aspire publish' command, the 'Type to Search' is visible even without having any selection on the publisher list.

[Coleen17]

INSTALL STEPS

1. Clean machine: Win11 x64 23h2 ENU
2. Install SDK 9.0.203
3. Add dotnet 9 feed for 9.2.0-preview.1
4. Install the latest Aspire 9.2.0-preview.1 templates dotnet new install Aspire.ProjectTemplates::9.2.0 --force
5. Run the command using powershell (admin): iex "& { $(irm https://aka.ms/install-artifacts-credprovider.ps1) }"
6. Install aspire.cli tool dotnet tool install --global aspire.cli --prerelease --source https://pkgs.dev.azure.com/dnceng/internal/_packaging/darc-int-dotnet-aspire-289c6b87/nuget/v3/index.json

REPRO STEPS

1. Open CMD and run the command: aspire new
2. Select a project template > Enter the project name > Enter the output path > Project templates version
3. Run the following command: cd aspire/project.apphost
4. Run the project using this command: aspire run
5. Publish the project using the command: aspire publish

ACTUAL The "Type to Search" is visible even without any publisher available on the selection list.

EXPECTED The 'Type to Search' will be disabled/remove if there is only one available on the selection list.