Revert "Report multiple in-process primary connections"

This reverts commit ac74a023.

Reason for revert: b/321958039 reported a benchmark regression.  However, the benchmark is private and opaque so it's not possible to know why the metric regressed.  This is especially puzzling because these changes only execute when a database is opened, which is usually once per process.

Change-Id: I254212f99dfe6a59ebfb95e594824dec9ee15600