Don't use Grafana for logs. Its (or any other basically, including Kibana or Graylog) interface sucks and I used Metabase which has much more friendly interface to show logs in tabular format instead of throwing raw logs like the others.
I collect logs with Vector on each instances and sent to central ClickHouse which Metabase reads from.
My services usually produce around 2GB of log data per day. From quick read on the CH I beleive it should not be a problem. Not sure how big the database it is but zip compressed log data is around that size for entire month.
I think Loki is pretty much the easiest thing you can find (if you want it to be multi server, at least).
Loki whole approach comes down to avoiding expensive indexing (compared to Elastic search et all.), and really on "grep" for searching instead.
I collect logs with Vector on each instances and sent to central ClickHouse which Metabase reads from.