Feature Request - Social plugin: Use the Jetpack logo in the sidebar of the post editor

### Impacted plugin

Social

### What

In the post editor, use the Jetpack logo so the UI is closer to what it is when only Jetpack is installed.

Internal Slack: p1727801160225789-slack-C02JJ910CNL

### How

Solutions:
- Use the default Jetpack logo
- Use a modified Jetpack logo with the Social logo being a tiny little badge on top of it

Having two different logos can be confusing to users, makes it more tedious to provide support when guiding users, and makes it harder for [the support doc](https://github.com/Automattic/jedi-jetpack-enhancements-of-docs-for-ai/issues/263).

| Jetpack plugin | Social plugin |
| ------------- | ------------- |
| | |

Review the screenshots and locate the Social plugin’s post-editor sidebar and its current logo definition. Compare it with the Jetpack presentation, resolve whether to use the default logo or a badged variant, and confirm that the sidebar branding is consistent with Jetpack while preserving the Social identity.

Written by the indexing model from the issue text.