Identity server errors during 3PID invite cause 500 internal server error

### Description

When an identity server returns a non-2xx response (my case: 400, `M_THREEPID_IN_USE`) to Synapse's `/store-invite` request during a 3PID invite, Synapse returns a 500 internal server error with `M_UNKNOWN` instead of handling the error and returning an appropriate 4xx response. Because the server always returns a generic 500 `M_UNKNOWN` here, it’s difficult for clients to implement good UX for this case.

### Steps to reproduce

- Make the identity server return 400 for /store-invite requests
- Do the request
- Synapse returns a 500 internal server error with `M_UNKNOWN` instead of handling the identity server's error response.

### Homeserver

On private homeserver

### Synapse Version

1.140.0

### Installation Method

Other - Helm chart

### Database

PostgreSQL 17.6

are you using a single PostgreSQL server or [separate servers for main and state](https://element-hq.github.io/synapse/latest/usage/configuration/config_documentation.html#databases)?
**Single**

have you previously ported from SQLite using the Synapse "portdb" script?
**No**

have you previously restored from a backup?
**No**

### Workers

Multiple workers

### Platform

In self-managed k8s in Ubuntu 24.04.3 VM (AMD) cluster

### Relevant log output

```shell
{"log":"Failed handle request via 'RoomMembershipRestServlet': ","namespace":"synapse.http.server","level":"ERROR","time":1764584153.74,"request":"POST-1566538","server_name":"homeserver.xx","ip_address":"11.11.11.11","site_tag":"8083","requester":"@65349:homeserver.xx","authenticated_entity":"@65349:homeserver.xx","method":"POST","url":"/_matrix/client/v3/rooms/!SFSEJVodkvUDxGipWt%3Ahomeserver.xx/invite","protocol":"HTTP/1.1","user_agent":"Mozilla/5.0 (Macintosh; Intel Mac OS X 10_15_7) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/142.0.0.0 Safari/537.36","exc_type":"HttpResponseException","exc_value":"400: Bad Request"}
```

Start at the RoomMembershipRestServlet entry point from the log and trace handling of the identity server's /store-invite response when it returns 400 M_THREEPID_IN_USE. Reproduce the request with a non-2xx identity-server response and determine the expected 4xx response instead of 500 M_UNKNOWN. Done means this failure is handled appropriately and covered by a regression test.

Written by the indexing model from the issue text.