Improve new search experience further

### Your use case

Following on from #21121, the new search could bring users a richer experience. This is a high level task to summarise stretch goals and other improvements which were considered for the initial release and didn't make it. These improvements will need product and design input before implementation.

The following items are phrased in the standard framework we use for enhancements:
* As a community user, I would like to be able to search public spaces to find communities which are relevant to me.
* As a user in 500 odd rooms, I would like to be able to find rooms based on partial name matches because I cannot remember the exact names of most of my rooms. These are subtasks for this item:
* Test harness for fuzzy search
- #21640
- Propose initial criteria for fuzzy search
- Will be closed as part of this issue:
- #14410

### Have you considered any alternatives?

_No response_

### Additional context

As part of this issue, these issues should also be considered:
- #21710