Logs services are miserably complicated. The 422 you got was because we had to temporarily disable log querying due to an API outage this morning, for example. They should be working better now (we just re-enabled the logs endpoint).
LogDNA does free log tailing if that’s most what you need.
The simplest ready to go log setup is Loki and it’s still two components + s3: GitHub - grafana/loki: Like Prometheus, but for logs.
If I were trying to do simple logs, I might consider just subscribing to NATs and writing stuff to sqlite files with the full text extension: SQLite FTS5 Extension
NATs has clients for most runtimes, and you can just connect directly to our NATS service if you want: Fly Logs over NATS