Can you clarify what your concern is with "heavy" logging solutions that require database/elasticsearch? If you're worried about system resources that's one thing, but if it's just that it seems "complicated," I have a docker compose file that handles Graylog, Opensearch, and Mongodb. Just give it a couple of persistent storage volumes, and it's good to go. You can send logs directly to it with syslog or gelf, or set up a filebeat container to ingest file logs.
There's a LOT you can do with it once you've got your logs into the system, but you don't NEED to do anything else. Just something to consider!