fix(app): preserve host badge identity

Keep host badges visible under row pressure and apply the selected host color consistently to the icon, label, and tinted background.

packages/app/src/components/sidebar/host-badge.tsx

@@ -1,13 +1,32 @@
-import { Text, View } from "react-native";
+import { Text, View, type TextStyle, type ViewStyle } from "react-native";
 import { StyleSheet, withUnistyles } from "react-native-unistyles";
 import { Server } from "lucide-react-native";
 import { HOST_COLORS, type HostColor } from "@/hosts/appearance";
-import { identityColor } from "@/styles/identity-colors";
+import { identityColor, identityTint } from "@/styles/identity-colors";
 import type { Theme } from "@/styles/theme";
 
 const ThemedServer = withUnistyles(Server);
 const MAX_NAMED_BADGE_WIDTH = 96;
 
+interface HostBadgeColorOverride {
+  badge: ViewStyle | null;
+  text: TextStyle | null;
+}
+
+function buildColorOverrides(): Record<HostColor, HostBadgeColorOverride> {
+  const byColor = {} as Record<HostColor, HostBadgeColorOverride>;
+  for (const color of HOST_COLORS) {
+    byColor[color] =
+      color === "none"
+        ? { badge: null, text: null }
+        : {
+            badge: { backgroundColor: identityTint(color) },
+            text: { color: identityColor(color) },
+          };
+  }
+  return byColor;
+}
+
 // The identity table is theme-independent, so its icon mapping is fixed for the life of the
 // module. It must not be rebuilt per render: a fresh `uniProps` identity makes withUnistyles
 // re-subscribe every pass.
@@ -22,6 +41,7 @@ function buildIconMappings(): Record<HostColor, (theme: Theme) => { color: strin
   return byColor;
 }
 
+const COLOR_OVERRIDES = buildColorOverrides();
 const ICON_MAPPINGS = buildIconMappings();
 
 /**
@@ -41,14 +61,19 @@ export function HostBadge({
   color: HostColor;
   showLabel: boolean;
 }) {
+  const override = COLOR_OVERRIDES[color];
   return (
     <View
-      style={[hostBadgeStyles.badge, showLabel ? null : hostBadgeStyles.badgeIconOnly]}
+      style={[
+        hostBadgeStyles.badge,
+        showLabel ? null : hostBadgeStyles.badgeIconOnly,
+        override.badge,
+      ]}
       testID={`sidebar-host-badge-${serverId}`}
     >
       <ThemedServer size={9} uniProps={ICON_MAPPINGS[color]} />
       {showLabel ? (
-        <Text style={hostBadgeStyles.text} numberOfLines={1}>
+        <Text style={[hostBadgeStyles.text, override.text]} numberOfLines={1}>
           {label}
         </Text>
       ) : null}
@@ -71,7 +96,7 @@ const hostBadgeStyles = StyleSheet.create((theme) => ({
     backgroundColor: theme.colors.surface2,
     maxWidth: MAX_NAMED_BADGE_WIDTH,
     minWidth: 0,
-    flexShrink: 1,
+    flexShrink: 0,
   },
   // Icon-only drops the label, so the asymmetric padding that made room for text leaves a
   // lopsided pill. Symmetric padding recenters the icon.