From personal experience, it scales very well vertically. Have a system in production with tens of billions of rows and north of 12 TB of storage total. That system is read-heavy with large batched inserts, not many deletes or updates.

Biggest limiter is memory, where the need for it grows linearly with table index size. Postgres really really wants to keep the index pages hot in the OS cache. Gets very sad and weird if it can’t: will unpredictably resort to table scans sometimes.

We are running on AWS Aurora, on a db.r6i.12xlarge. Nowhere even close to maxed out on potential vertical scaling.