The launcher redesign showed the All Games pill count from the full bundled
catalog. That made the counter report every row in game.db even though the All
Games filter itself only shows games that are visible on the current network or
present locally.
Use the same network-visible predicate for the counter and the filter. The pill
count and results total now describe the displayed network library instead of
the baked catalog size.
Test Plan:
- git diff --check
Refs: user redesign nitpick about All Games counter