It's not clear that if a pattern is synced, then it does not show up in the Patterns Inserter. In the example below, I've created three patterns — two of which are "synced". Consequently, those two are omitted from the Pattern Inserter.
If I create a pattern, I think it should be available in the Inserter, as it is within the Library, synced or not.
Proposal
Perhaps we can include an indicator of synced status in the preview, similar to how Openverse media has an ellipsis for more actions — or a treatment like badges in List view.

It's not clear that if a pattern is synced, then it does not show up in the Patterns Inserter. In the example below, I've created three patterns — two of which are "synced". Consequently, those two are omitted from the Pattern Inserter.
If I create a pattern, I think it should be available in the Inserter, as it is within the Library, synced or not.
Proposal
Perhaps we can include an indicator of synced status in the preview, similar to how Openverse media has an ellipsis for more actions — or a treatment like badges in List view.