Initial and incremental syncs with presence enabled eat up RAM until an OOM hits

This issue has been migrated from [#13901](https://github.com/matrix-org/synapse/issues/13901).

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### Description

Synapse eat all ram (8GB) and swap until OOM hits.

### Steps to reproduce

There are 3 accounts on the server. This happens when one of the users connects (my account is an administrator). Did not connect to other rooms with a large number of connections before the problem occurred.

### Homeserver

tavda.org

### Synapse Version

{"server_version":"1.67.0","python_version":"3.10.6"}

### Installation Method

Debian packages from packages.matrix.org

### Platform

Ubuntu 22.04 LTS

### Relevant log output

```shell
Sep 26 14:27:29 nether2.network systemd[1]: matrix-synapse.service: A process of this unit has been killed by the OOM killer.
Sep 26 14:27:30 nether2.network systemd[1]: matrix-synapse.service: Main process exited, code=killed, status=9/KILL
Sep 26 14:27:30 nether2.network systemd[1]: matrix-synapse.service: Failed with result 'oom-kill'.
Sep 26 14:27:30 nether2.network systemd[1]: matrix-synapse.service: Consumed 29.476s CPU time.
Sep 26 14:27:33 nether2.network systemd[1]: matrix-synapse.service: Scheduled restart job, restart counter is at 15.
Sep 26 14:27:33 nether2.network systemd[1]: Stopped Synapse Matrix homeserver.
Sep 26 14:27:33 nether2.network systemd[1]: matrix-synapse.service: Consumed 29.476s CPU time.
Sep 26 14:27:33 nether2.network systemd[1]: Starting Synapse Matrix homeserver...
Sep 26 14:27:39 nether2.network synapse[8680]: root: [main] ***** STARTING SERVER *****
Sep 26 14:27:39 nether2.network synapse[8680]: root: [main] Server /opt/venvs/matrix-synapse/lib/python3.10/site-packages/synapse/app/homeserver.py version 1.67.0
Sep 26 14:27:39 nether2.network synapse[8680]: root: [main] Server hostname: tavda.org
Sep 26 14:27:39 nether2.network synapse[8680]: root: [main] Instance name: master
Sep 26 14:27:39 nether2.network synapse[8680]: synapse.app.homeserver: [main] Setting up server
Sep 26 14:27:39 nether2.network synapse[8680]: synapse.server: [main] Setting up.
Sep 26 14:27:39 nether2.network synapse[8680]: synapse.storage.databases: [main] [database config 'master']: Checking database server
Sep 26 14:27:39 nether2.network synapse[8680]: synapse.storage.databases: [main] [database config 'master']: Preparing for databases ['main', 'state']
Sep 26 14:27:39 nether2.network synapse[8680]: synapse.storage.prepare_database: [main] ['main', 'state']: Checking existing schema version
Sep 26 14:27:39 nether2.network synapse[8680]: synapse.storage.prepare_database: [main] ['main', 'state']: Existing schema is 72 (+8 deltas)
Sep 26 14:27:39 nether2.network synapse[8680]: synapse.storage.databases.main: [main] Checking database for consistency with configuration...
Sep 26 14:27:39 nether2.network synapse[8680]: synapse.storage.prepare_database: [main] Applying schema deltas for v72
Sep 26 14:27:39 nether2.network synapse[8680]: synapse.storage.prepare_database: [main] Schema now up to date
Sep 26 14:27:39 nether2.network synapse[8680]: synapse.storage.databases: [main] [database config 'master']: Starting 'main' database
```

### Anything else that would be useful to know?

During normal server operation, the top shows 7.5GB of free memory. The other two users can communicate with each other.