chore: add connect reason

[levkk]

Log a reason for which a server connection was created. This helps debug configuration.

[codecov]

Codecov Report

❌ Patch coverage is 81.42857% with 13 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
.../src/backend/replication/logical/publisher/slot.rs	0.00%	7 Missing ⚠️
pgdog/src/backend/connect_reason.rs	81.81%	2 Missing ⚠️
pgdog/src/admin/probe.rs	0.00%	1 Missing ⚠️
pgdog/src/backend/pub_sub/listener.rs	0.00%	1 Missing ⚠️
...c/backend/replication/logical/subscriber/stream.rs	0.00%	1 Missing ⚠️
pgdog/src/backend/server.rs	95.00%	1 Missing ⚠️

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[blacksmith-sh]

Found 1 test failure on Blacksmith runners:

Failure

Test	View Logs
pg_tests/TestTimeout	View Logs