Optimize OverlayManagerSettings dump

Currently dumping the OverlayManagerSettings uses streams, and could
lead to at most 3 traversals over all the items. This optimizes the
dumping to one single traversal, without streams.

Flag: EXEMPT refactor
Bug: 391829821
Test: atest InstallOverlayTests#testAdbShellOMSInterface
Change-Id: Ia21debd1538d4e792862aeb7e86c1f21de2f5e54