Most ID selectors (like e.g. the 'target' ones in constraints and modifiers) do not show difference between local and linked IDs. Even worse, they do not allow to select linked ones when a local one exists with the same name.
This has been the case since ages, but with library overrides that now systematically generate those kind of local/linked same-name couples of IDs, it's becoming even more annoying.
Obvious solution would be to show the L prefix for linked data, and to decouple shown name from the one used to actually select the ID.
A first simple & stupid attempt to fix this was rB4669c3692cc4: Add library-hint to datablock search menus. (this had to be reverted), but unfortunately the issue is more complex and requires more involved changed in the UI menu code…