Site Editor: Preserve block search state when returning from a block in Styles

[smhz101]

When working in the Site Editor under Styles > Blocks, the search field is useful for finding related blocks.

The problem is that the search is cleared after opening one of the results and then going back to the Blocks list.

For example, if I search for "Post", open the Post Title block, make or review some style changes, and then go back, the search field is empty again and the full list of blocks is shown.

When working through several related blocks, this means entering the same search again after every block.

I think the previous search should be preserved when returning to the Blocks screen.

Steps to reproduce

1. Open Appearance > Editor.
2. Open Styles.
3. Go to Blocks.
4. Search for something, for example "Post".
5. Open one of the blocks from the search results.
6. Open or change its styles.
7. Go back to the Blocks list.

Current result

The previous search is cleared and the full list of blocks is shown.

Expected result

The search term should still be present and the previous filtered results should still be shown.

For example:

Search "Post"
-> Open Post Title
-> Edit/review styles
-> Go back
-> Search "Post" is still active

This would make it easier to work through multiple related blocks without having to repeat the same search every time.