I use Promtail+Loki+Grafana on my home server, which is decently performant, light on resources and storage, and searchable. It takes a little effort to learn the LogQL query language, but it's very expressive.

I'm running it on Kubernetes, but it should be pretty straightforward to configure for running on plain Docker.

At work we use the syslog log driver for docker. Essentially any container stdout gets pushed in to the system syslog that then gets ingested into splunk through one of their forwarders. We needed more than just container logs so that's the reason for that. For a home setup I'd probably do the same but use the ELK stack instead of splunk.

Though not particularly a logging solution, lazydocker has made docker administration a lot easier for me.

Also not really a solution but Dozzle has been awesome for making viewing live container logs easier

Lol as bad as it is, just reading what's output to stdout. Worst case, tailing it via a terminal. I do want/need to actually implement a proper solution at some point, but I haven't actually pulled the trigger on beginning the hunt for a solution yet.

Not sure if it answers your question, but I use Portainer to check the different docker containers I am running. It does not allow me to check the 'docker-runtime' logs themselves though, only the logfiles of each of the running containers. It also allows easy term connection if you want, although I usually do that directly form the terminal itself.