Having said that, both PostgreSQL and Microsoft SQL has 8KB page size, while original SQLite had 1KB pages, before switching to 4KB, while still supporting 64KB pages. On top of that, Microsoft SQL operates internally on extents of 8 pages (64 KB) instead of a single page, but still pretends to use 4 KB pages [2].
In other words - no idea.
[1] https://www.postgresql.org/docs/current/storage-page-layout....
[2] https://learn.microsoft.com/en-us/sql/relational-databases/p...
[0] There's even some cool research about B-trees that have the layout depend on the probabilistic distribution of the lookups: https://dl.acm.org/doi/10.1145/3592980.3595316
Maybe that’s why ?
That said, there is no universal page size one can choose from. Some workloads will benefit from smaller page size while others will benefit from larger page size but 512K is not the size you will want to choose. Read-, write-, space-amplification, CPU cache thrashing etc.