[Prep] Threads: Threads catchup mechanism

### Description

In the context of threads 2.0, we want a smart mechanism to update threads. We need such mecanisms for several reasons:
- update the unread status
- compute mention badge
- update the thread list in the activity center ( https://github.com/element-hq/element-meta/issues/2768)

We need SSS to provide threads updates in an efficient way.

# Acceptance criteria
- TBD

# Dependencies
- None

# Out of scope
- EX could do like for threads 1.0 with `/relations` or back paginate the entire room to previous known event but we know it is not usable for the end users.
- [We expimented it](https://github.com/element-hq/element-meta/issues/2809#issuecomment-2827744073) but the performance does not make it usable

# Subtasks
### MSC
* https://github.com/matrix-org/matrix-spec-proposals/pull/4360

### Synapse
* https://github.com/element-hq/synapse/issues/18436
* https://github.com/element-hq/synapse/pull/19041

### Rust
* https://github.com/matrix-org/matrix-rust-sdk/issues/5039

### Other
*

Start by reading MSC PR 4360, Synapse issue 18436 and PR 19041, and Rust SDK issue 5039 to understand the proposed catchup mechanism. The issue provides no acceptance criteria, so the completion conditions still need to be defined across those related work items.

Written by the indexing model from the issue text.