If replica server cannot execute queries fast enough, a specialized (optimized for OLAP-workload) database should be used instead. This can be a cloud service (like BigQuery, Redshift, Snowflake, Motherduck) or self-hosted solutions (ClickHouse, PostgreSql with pg_analytics extension, or even in-process DuckDB). Data sync is performed either with scheduled full-copy (simple, but not suitable for near real-time analytics) or via CDC (see Airbyte).
1) Read replicas with copied data. The most straightforward, allowing using the same SQL syntax and tooling. Examples: Postgres read replica and BemiDB (disclaimer: I'm a contributor)
2) Operational databases with integrations. Designed for sub-second real-time, bring their own extended SQL syntax for things like window functions. Examples: Materialize and RisingWave
3) Analytical databases with syncing. Allow writing and reading directly, optimized for analytical workloads. Examples: ClickHouse and DuckDB
4) Data warehouses with ETL. Great for large volumes of data, traditionally used with ETL batch processing. Examples: Snowflake and Redshift