### What problem does this PR solve?
This PR closing feature request #11286.
It implements ability to choose the background theme of the _Full screen
chat_ which is Embed into webpage.
Looks like that:
<img width="501" height="349" alt="image"
src="https://github.com/user-attachments/assets/e5fdfb14-9ed9-43bb-a40d-4b580985b9d4"
/>
It works similar to `Locale`, using url parameter to set the theme.
if the parameter is invalid then is using the default theme.
### Type of change
- [x] New Feature (non-breaking change which adds functionality)
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Co-authored-by: Your Name <you@example.com>
088b049b4c