fix(dbmanager): keep the pool alive across errors and restarts

Implements the fixes from audit/pkg/dbmanager.audit.md.

- Stop closing the shared *sql.DB to recover from errors. Adapter
  factories and the health checker no longer call Reconnect; Reconnect is
  atomic and operator-only.
- Postgres uses a custom driver.Connector: Reconnect retires pooled
  connections by generation without closing the pool, so held Bun/GORM
  handles keep working. Verified against a live server restart.
- Add TCP keepalive, TCP_USER_TIMEOUT, a bounded reuse ping and
  statement_timeout as a runtime parameter; drop the 2 min timeout floor.
- Health check pings without holding the connection lock.
- Listener: single goroutine pair, bounded Close without UNLISTEN, and
  serialised use of the pgx connection (fixes conn busy and a close race).
- Fix Connect/Close/Connect/Close panic, idempotent Connect, dial outside
  the manager lock, clean up on partial failure.
- SQLite: pin :memory: to one connection, pragmas via DSN.
- Escape credentials in Postgres/MSSQL/Mongo DSNs; sslmode defaults to
  prefer. Wire retry settings, publish metrics, fix logger calls.
- NewConnectionFromDB: Close is a no-op with a warning (caller owns the
  pool); Reconnect only pings.
- Document correct usage in the README; mark the audit with what was done.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>

pkg/dbmanager/providers/mssql.go

@@ -35,12 +35,11 @@ func (p *MSSQLProvider) Connect(ctx context.Context, cfg ConnectionConfig) error
 	var db *sql.DB
 	var lastErr error
 
-	retryAttempts := 3 // Default retry attempts
-	retryDelay := 1 * time.Second
+	retryAttempts, retryDelay, retryMaxDelay := retryPolicy(cfg)
 
 	for attempt := 0; attempt < retryAttempts; attempt++ {
 		if attempt > 0 {
-			delay := calculateBackoff(attempt, retryDelay, 10*time.Second)
+			delay := calculateBackoff(attempt, retryDelay, retryMaxDelay)
 			if cfg.GetEnableLogging() {
 				logger.Info("Retrying MSSQL connection: attempt=%d/%d, delay=%v", attempt+1, retryAttempts, delay)
 			}
@@ -57,7 +56,7 @@ func (p *MSSQLProvider) Connect(ctx context.Context, cfg ConnectionConfig) error
 		if err != nil {
 			lastErr = err
 			if cfg.GetEnableLogging() {
-				logger.Warn("Failed to open MSSQL connection", "error", err)
+				logger.Warn("Failed to open MSSQL connection: %v", err)
 			}
 			continue
 		}
@@ -71,7 +70,7 @@ func (p *MSSQLProvider) Connect(ctx context.Context, cfg ConnectionConfig) error
 			lastErr = err
 			db.Close()
 			if cfg.GetEnableLogging() {
-				logger.Warn("Failed to ping MSSQL database", "error", err)
+				logger.Warn("Failed to ping MSSQL database: %v", err)
 			}
 			continue
 		}