Update split config when launch adjacent in non-default displays

Split layout config should be updated when launch adjacent is called in
non-default displays. This CL updates the config before preparing to
move the split root to current display.

Bug: 438285797
Test: manual && atest WMShellUnitTests
Flag: com.android.window.flags.enable_non_default_display_split
Change-Id: Iafe3d3c97ddcd18e4acdb0b12b770c6e8526cb70