Exact strategy to be determined—we're looking at various data layers at the moment. I wish we could do something simple like a rotating log file, but we want to be able to query it in the app (for instance, to show recent logins).
Have you considered an OLAP database like Clickhouse or QuestDB? An OLAP database would be a much better fit for audit tables given the read and append-only writing requirements, would compress better, and you might be able to fit it directly without changing any app code with a Postgresql foreign data wrapper.
You can partition your audit/event table by time period and archive old events [1] or you can avoid the records hitting the database in the first place by generating the events elsewhere to begin with [2].