SynapseError: 429 - Too Many Requests

This issue has been migrated from [#14180](https://github.com/matrix-org/synapse/issues/14180).

---

### Description

Hello everyone,
I saw some issues on github talking about exactly this behaviour unfortunately when I try to invite people in a room it takes ages until synapse sends invites, I find the following errors in the logs.
```
2022-10-14 07:12:48,276 - synapse.http.server - 107 - INFO - POST-99625 - SynapseError: 429 - Too Many Requests
2022-10-14 07:12:53,621 - synapse.http.server - 107 - INFO - POST-99644 - SynapseError: 429 - Too Many Requests
2022-10-14 07:13:00,212 - synapse.http.server - 107 - INFO - POST-99648 - SynapseError: 429 - Too Many Requests
2022-10-14 07:13:05,965 - synapse.http.server - 107 - INFO - POST-99654 - SynapseError: 429 - Too Many Requests
2022-10-14 07:13:11,876 - synapse.http.server - 107 - INFO - POST-99667 - SynapseError: 429 - Too Many Requests
2022-10-14 07:13:17,777 - synapse.http.server - 107 - INFO - POST-99671 - SynapseError: 429 - Too Many Requests
2022-10-14 07:13:23,692 - synapse.http.server - 107 - INFO - POST-99678 - SynapseError: 429 - Too Many Requests
```
All the rooms and spaces are actually on our own server and we never invite people from other servers. I also tried to up the federation limit in the config with no change:
```
# The maximum number of concurrent federation requests allowed
# from a single server
federation_rc_reject_limit: 500
```
This started to happen when we created a lot of individual rooms for setting up our communication environment. I am using element.io as client and running the whole stack as docker containers behind the reverse proxy traefik 2, all on the latest version.

Is there any config I need to change in order for this to work?

Thank you in advance for any help.
BR,
Loris

### Steps to reproduce

- create a lot of rooms and inviting 3 people
- no external server or user invitied

### Homeserver

asemes.matrix.lu

### Synapse Version

{"server":{"name":"Synapse","version":"1.68.0"}}

### Installation Method

Docker (matrixdotorg/synapse)

### Platform

Ubuntu 22.04.01 LTS 64 bit
Dell R720
Client: Docker Engine - Community
Version: 20.10.18
API version: 1.41
Go version: go1.18.6
Git commit: b40c2f6
Built: Thu Sep 8 23:11:43 2022
OS/Arch: linux/amd64
Context: default
Experimental: true

Server: Docker Engine - Community
Engine:
Version: 20.10.18
API version: 1.41 (minimum version 1.12)
Go version: go1.18.6
Git commit: e42327a
Built: Thu Sep 8 23:09:30 2022
OS/Arch: linux/amd64
Experimental: false
containerd:
Version: 1.6.8
GitCommit: 9cd3357b7fd7218e4aec3eae239db1f68a5a6ec6
runc:
Version: 1.1.4
GitCommit: v1.1.4-0-g5fd4c4d
docker-init:
Version: 0.19.0
GitCommit: de40ad0

Running in docker containers with postgres14, traefik 2.X, vectorim/element-web:latest and matrixdotorg/synapse:latest.

### Relevant log output

```shell
2022-10-14 07:12:48,276 - synapse.http.server - 107 - INFO - POST-99625 - SynapseError: 429 - Too Many Requests
2022-10-14 07:12:53,621 - synapse.http.server - 107 - INFO - POST-99644 - SynapseError: 429 - Too Many Requests
2022-10-14 07:13:00,212 - synapse.http.server - 107 - INFO - POST-99648 - SynapseError: 429 - Too Many Requests
2022-10-14 07:13:05,965 - synapse.http.server - 107 - INFO - POST-99654 - SynapseError: 429 - Too Many Requests
2022-10-14 07:13:11,876 - synapse.http.server - 107 - INFO - POST-99667 - SynapseError: 429 - Too Many Requests
2022-10-14 07:13:17,777 - synapse.http.server - 107 - INFO - POST-99671 - SynapseError: 429 - Too Many Requests
2022-10-14 07:13:23,692 - synapse.http.server - 107 - INFO - POST-99678 - SynapseError: 429 - Too Many Requests
```
```

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

_No response_

Start by reproducing the invite requests to /_matrix/client/r0/rooms/.../invite while reviewing the Synapse logs and the federation_rc_reject_limit setting. Compare the local-only room scenario with the reported 429 responses and determine which rate limit is responsible; done means identifying the applicable configuration or confirming that the behavior is expected.

Written by the indexing model from the issue text.