In addition a kind of query for namespaces is needed.

• Who has a partial block on templates, modules, article main space?

This could be implemented by automatically assigning a tag to every log entry corresponding with the creation, deletion, and change from/to a partial block.

This would not solve the second case though.

@MGChecker Anti-Harassment tools team is winding down its work on partial blocks and preparing to move on to making improvements to CheckUser. In light of that, we are not prioritising new feature development on this project for now. We would be happy to provide guidance if a volunteer decides to take this on.

The information if a block was partial or sidewide is only stored in the param blob of the log.

The information must be stored in the log_search database table and than could be used to search.

The active partial blocks can be seen by Special:BlockList with type = partial