Data/config file errors when using Docker volumes (and fly.io)

This issue has been migrated from [#14122](https://github.com/matrix-org/synapse/issues/14122).

---

I've already used the `generate` command to get a valid `homeserver.yaml` file (which I then pulled from the local volume on my machine).

My `Dockerfile`:
```Dockerfile
FROM matrixdotorg/synapse:v1.68.0

ENV SYNAPSE_SERVER_NAME=matrix.my.domain
ENV SYNAPSE_REPORT_STATS=no

WORKDIR /data
COPY homeserver.yaml .
RUN chown -R $UID:$GID .
```
However, when trying to run, I get the following error:
```
Config file '/data/homeserver.yaml' does not exist.
```

I am deploying on https://fly.io/; I have a volume mount for `/data` that I'm pretty sure is empty (I deleted and recreated it several times), but I am not able to write to the volume directly because Fly does not allow that. The application has to do all writing, but I don't think Synapse supports this with this config file setup?

I figured I could set `SYNAPSE_CONFIG_DIR` env var to `/config` (and then change `WORKDIR /data` to `WORKDIR /config`) so that it wouldn't conflict with the volume, but that gives me another error:
```
PermissionError: [Errno 13] Permission denied: '/data/matrix.my.domain.log.config'
[info] Generating log config file /data/matrix.my.domain.log.config which will log to /data/homeserver.log
```

So then I try editing `homeserver.yaml` and changing `log_config: "/data/matrix.my.domain.log.config"` to `log_config: "/config/matrix.my.domain.log.config"`, but all that does is change the error path:
```
PermissionError: [Errno 13] Permission denied: '/config/matrix.my.domain.log.config'
[info] Generating log config file /config/matrix.my.domain.log.config which will log to /config/homeserver.log
```

If anyone has any ideas for me to try, I'd appreciate it! 😄

Read the Dockerfile and homeserver.yaml paths first, then inspect how the Synapse container handles /data, SYNAPSE_CONFIG_DIR, log_config, and mounted-volume permissions. Reproduce the startup errors with the stated image and Fly.io volume setup; done means the configuration starts without missing-file or PermissionError failures.

Written by the indexing model from the issue text.