[Experiment] Remove "Load Latest" button (#7120)

* Remove "show latest" behind the gate

* Add HomeBadgeProvider

* Update provider state from home feed tabs

* Add Home badge to native

* Add Home badge to mobile web

* Add Home badge to desktop web

src/view/com/util/load-latest/LoadLatestBtn.tsx

@@ -9,6 +9,7 @@ import {useMinimalShellFabTransform} from '#/lib/hooks/useMinimalShellTransform'
 import {usePalette} from '#/lib/hooks/usePalette'
 import {useWebMediaQueries} from '#/lib/hooks/useWebMediaQueries'
 import {clamp} from '#/lib/numbers'
+import {useGate} from '#/lib/statsig/statsig'
 import {colors} from '#/lib/styles'
 import {isWeb} from '#/platform/detection'
 import {useSession} from '#/state/session'
@@ -34,6 +35,11 @@ export function LoadLatestBtn({
   // move button inline if it starts overlapping the left nav
   const isTallViewport = useMediaQuery({minHeight: 700})
 
+  const gate = useGate()
+  if (gate('remove_show_latest_button')) {
+    return null
+  }
+
   // Adjust height of the fab if we have a session only on mobile web. If we don't have a session, we want to adjust
   // it on both tablet and mobile since we are showing the bottom bar (see createNativeStackNavigatorWithAuth)
   const showBottomBar = hasSession ? isMobile : isTabletOrMobile