Support enhanced notification settings

[richvdh]

The Riot team have a project to redesign the Notification settings in the app, and fix a number of bugs while we're at it: element-hq/element-web#13959.

This issue exists to track the work needed on the Synapse side to support it.

[richvdh]

Part of this work is/was #5745, though as of current writing it looks like we want to revisit that.

The current plan is https://docs.google.com/document/d/1pjYrGokTQGDZQLtagZvG4dY67RsjUdFDfpOzSiWtOBg/edit#heading=h.5bim93tvequg.

[richvdh]

Work that I think needs doing:

• updated implementation of unread-count tracking, to replace MSC2625 (this is Re-implement unread counts #7736)
• MSC2654 describing the new implementation, to replace MSC2625
• draft summarising changes to default push rules and migration and compatibility strategies (https://docs.google.com/document/d/1pjYrGokTQGDZQLtagZvG4dY67RsjUdFDfpOzSiWtOBg)
• trial implementations of new push rules? (Implement updated push rules #7960 Implement new experimental push rules #7997)
• MSC(s) for new push rules

[richvdh]

I think this work evolved into matrix-org/matrix-spec-proposals#2785 and then got parked.

[ShadowJonathan]

@richvdh Is this issue still applicable as that MSC, or do I need to open a separate issue to track implementation of that MSC?

[richvdh]

I don't think another issue saying "Implement MSC2785" is going to add any value.