downloadState requires server restart

*This issue was originally created by [**@bones-was-here**](https://github.com/bones-was-here) at .*

### Background information

- **Dendrite version or git SHA**: 0.13.3
- **SQLite3 or Postgres?**: postgres
- **Running in Docker?**: no
- **`go version`**: 1.21
- **Client used (if applicable)**: element web

### Description

- **What** is the problem: downloadState often hangs indefinitely unless dendrite is first restarted
- **Who** is affected: admins trying to fix room state issues
- **How** is this bug manifesting: curl doesn't exit until killed and doesn't receive any HTTP BODY, nothing is logged (except for request cancelled when curl is killed)
- **When** did this first appear: unknown, but it's quite old

### Steps to reproduce

- Unsure how to get the cache into a state where this will happen, but it seems more likely than not when doing downloadState

For a long time I didn't know why downloadState sometimes worked and other times just hung.
Is it possible that cache<>db synchronisation issues affect other aspects of server operation too? Related: https://github.com/matrix-org/dendrite/issues/3190