Store them in something like Google BigQuery, partitioned by day.

You pay very cheap for storage (since it is stored in Google Cloud Storage behind), almost nothing, and relatively somewhat expensive for each data you extract of the system.

No need for the interactive exploration, you can do queries on a case-by-case basis, worst case you pay to scan one day of logs (or less if you pay Reserved capacity, you pay a fixed price).

0 devops needed.

If you want a self-hosted big database that is easy and scalable for that usage, check ClickHouse.