Feature Request: Social Links Block - Add custom social icon option

### What

Social Links Block is limited to preset icons. What about adding an n+1 option to add a custom icon?

### Why

1- I just got a user in chat asking about adding an IMDB icon to the block. 34270343-hc
2- We have an open request to add a number of icons to the preset.

We can't include all icons but making it open-ended could add value to the block.

### How

We could add it to the end of the preset icon suggestions to avoid its overuse.

We could also rethink how to icon-search bar works: instead of searching for the icon first then having to add the link, we could just ask for the link and it will either auto-select the icon or offer the option to upload a new one.

Connecting this with the open request below makes sense:
- https://github.com/Automattic/wp-calypso/issues/39053

Start by reviewing the Social Links Block's preset icon suggestions and icon-search bar, then read the linked issue #39053 for related icon requests. Define whether the completed work adds a custom icon option, changes link-based icon selection, or both, and verify that the chosen behavior supports icons such as IMDB without relying only on presets.

Written by the indexing model from the issue text.