"Publish to Play" button becomes visible after the build profiles duplication

Steps to reproduce:

1. Create a new project
2. Go to File -> Build Profiles
3. Select the macOS platform and create a build
4. Return to the "Platforms" list and select "Web"
5. If a module is not installed, please install it
6. Create a build for it too
7. Verify that both builds are displayed under the "Build Profiles"
8. Select them both
9. Verify that you do not get any buttons in the details window
10. Duplicate both selected builds
11. Verify the result

Actual results: "Publish to Play" button becomes visible. A short video is added below in the "Attachments" section.

Expected results: No button.

Reproducible with versions: 6000.2.0a9, 6000.2.0a10

Not reproducible with versions: 6000.1.2f1, 6000.2.0a8

Can’t test with versions: -

Tested on (OS): M1 Max - Sequoia 15.4.1