502 error when looking up room alias from dead homeserver

### Description

Looking up a room alias hosted by a dead homeserver returns a 502 error.

This causes a CORS error for clients running in web browser, so eg. Element Web hangs.

### Steps to reproduce

```shell
$ curl 'https://matrix-client.matrix.org/_matrix/client/v3/directory/room/%23nonexistentroom%3Alibera.chat' -i
HTTP/2 502
date: Thu, 15 Feb 2024 23:35:59 GMT
content-type: text/plain; charset=UTF-8
content-length: 15
x-frame-options: SAMEORIGIN
referrer-policy: same-origin
cache-control: private, max-age=0, no-store, no-cache, must-revalidate, post-check=0, pre-check=0
expires: Thu, 01 Jan 1970 00:00:01 GMT
server: cloudflare
cf-ray: 85615ed20cfcd676-CDG

error code: 502
```

### Homeserver

matrix.org

### Synapse Version

1.101.0 (b=matrix-org-hotfixes,6dbedcf601)

### Installation Method

Docker (matrixdotorg/synapse)

### Database

postgresql

### Workers

Multiple workers

### Platform

n/a

### Configuration

_No response_

### Relevant log output

```shell
n/a
```

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

_No response_

Start by reproducing the room-alias lookup with the curl request in the issue and trace the Synapse endpoint handling a dead homeserver. Identify where the upstream failure becomes a 502, then verify that the response is handled correctly for browser clients without the reported CORS failure.

Written by the indexing model from the issue text.