chore(deps): update dependency element-hq/synapse to v1.147.0 (#3877)

This PR contains the following updates:

| Package | Update | Change |
|---|---|---|
| [element-hq/synapse](https://github.com/element-hq/synapse) | minor | `1.146.0` → `1.147.0` |

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### Release Notes

<details>
<summary>element-hq/synapse (element-hq/synapse)</summary>

### [`v1.147.0`](https://github.com/element-hq/synapse/releases/tag/v1.147.0)

[Compare Source](https://github.com/element-hq/synapse/compare/v1.146.0...v1.147.0)

### Synapse 1.147.0 (2026-02-10)

No significant changes since 1.147.0rc1.

### Synapse 1.147.0rc1 (2026-02-03)

#### Bugfixes

- Fix memory leak caused by not cleaning up stopped looping calls. Introduced in v1.140.0. ([#&#8203;19416](https://github.com/element-hq/synapse/issues/19416))
- Fix a typo that incorrectly made `setuptools_rust` a runtime dependency. ([#&#8203;19417](https://github.com/element-hq/synapse/issues/19417))

#### Internal Changes

- Prune stale entries from `sliding_sync_connection_required_state` table. ([#&#8203;19306](https://github.com/element-hq/synapse/issues/19306))
- Update "Event Send Time Quantiles" graph to only use dots for the event persistence rate (Grafana dashboard). ([#&#8203;19399](https://github.com/element-hq/synapse/issues/19399))
- Update and align Grafana dashboard to use regex matching for `job` selectors (`job=~"$job"`) so the "all" value works correctly across all panels. ([#&#8203;19400](https://github.com/element-hq/synapse/issues/19400))
- Don't retry joining partial state rooms all at once on startup. ([#&#8203;19402](https://github.com/element-hq/synapse/issues/19402))
- Disallow requests to the health endpoint from containing trailing path characters. ([#&#8203;19405](https://github.com/element-hq/synapse/issues/19405))
- Add notes that new experimental features should have associated tracking issues. ([#&#8203;19410](https://github.com/element-hq/synapse/issues/19410))
- Bump `pyo3` from 0.26.0 to 0.27.2 and `pythonize` from 0.26.0 to 0.27.0. Contributed by [@&#8203;razvp](https://github.com/razvp) @&#8203; ERCOM. ([#&#8203;19412](https://github.com/element-hq/synapse/issues/19412))

</details>

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Reviewed-on: https://gitea.alexlebens.dev/alexlebens/infrastructure/pulls/3877
Co-authored-by: Renovate Bot <renovate-bot@alexlebens.net>
Co-committed-by: Renovate Bot <renovate-bot@alexlebens.net>

clusters/cl01tl/helm/matrix-synapse/Chart.yaml

@@ -81,4 +81,4 @@ dependencies:
     repository: oci://harbor.alexlebens.net/helm-charts
 icon: https://cdn.jsdelivr.net/gh/selfhst/icons/png/matrix.png
 # renovate: datasource=github-releases depName=element-hq/synapse
-appVersion: 1.146.0
+appVersion: 1.147.0