Single node Postgres (with a beefy machine) can definitely manage in the 100k transactions per second. When you're pushing the high 100k into millions read replicas is a common approach.

When we're talking transactions, question of is it simply basic queries, bigger aggregations, and is it writes or reads. Writes if you can manage to do any form of multi-line insert or batching with copy you can push basic Postgres really far... From some benchmarks Citus as mentioned can hit millions of records per second safely with those approaches, and even without Citus can get pretty high write throughput.

Some apps might do just 1000 ops/second but still run on a distributed database for high availability or data locality reasons. For instance, shared-nothing databases usually guarantee RPO=0 (no data loss, recovery point objective) with RTO (recovery time objective) measured in seconds for zone and region-level outages. As for data locality, think automatic data placement/pinning to regions/data centers for data regulatory and low latency reasons (serve read/write requests equally fast for folks living in NYC, London, Tokyo).