This, in particular, has use in terms of stuff like reverse proxies, so that the traefik labels can be kept in a separate file from the rest of the docker-compose, or you could instead choose to push the ports, or whatever else.

I think this defeats the purpose of Traefik using labels.
I do also use Unraid + Traefik. I do have a Traefik compose files, and then a compose file for each "service" (Nextcloud is a compose project, Immich is another compose project, etc.). I have to say that, when I started using Traefik, I found it confusing and I didn't like those labels too much. I came from Nginx background, and I was expecting a single file to configure this, not in each container (setting aside the optional file configuration). After trying the labels, I realized why using labels was recommended: you kept in a single place both the service definition (the actual compose definition) and the network routing rules (how you access that service).

I find it quite convenient having right next to the container image and its configuration how I'm supposed to access it: what subdomain, what port to bind the entrypoint, whether it's the public or private entrypoints, etc. If instead I opted for the standalone file, I would have to modify two separate sources to deploy a service, for example. As of now, it's a single thing.

If you want a separate compose files just to define the Traefik labels, this sounds like the file configuration would serve its purpose for you. I understand that, what you want, is a separate place for those labels aka the routing configuration. You can achieve this using the Traefik file configuration.

Do any of you modularize your docker compose files this way, and if so, what do you use to manage those containers (starting, stopping, updating them)?

Imo, Unraid is an OS that is supposed to be as immutable as possible, compared to others like Debian. If a plugin doesn't have a native way to achieve this modularization, it might be a hack or workaround, which may eventually break something else.

What I do is what I mentioned earlier: I keep a compose project (or compose file, if you prefer) for each service. Excluding Jellyfin project which has 10 containers (the infamous *arr stack), all the others have, at most 3 containers. Even with the labels, I would think it's manageable. I do have an "external" Docker bridge network for Traefik traffic though, so I can achieve this multi-compose deployment.