feat(applications): add applications list page with host count and delete modal

- API: ApplicationWithCounts struct + get_applications_with_counts() — counts
  distinct hosts linked via matching ports (application_ports ↔ host_ports)
- ApplicationsPage at /applications: inline add form, table with Name and
  Hosts columns, delete confirmation modal showing affected host count
- Nav: add Applications link

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/api/applications.rs

@@ -1,11 +1,56 @@
 // api/applications.rs — Server functions for applications and their port associations
 
 use leptos::prelude::*;
+use serde::{Deserialize, Serialize};
 
 use crate::models::Application;
 
+// Application row enriched with the number of hosts that use at least one of
+// its registered ports.  Host count is computed via the join:
+//   application_ports → host_ports (matched on port_number) → hosts
+#[derive(Clone, Debug, Serialize, Deserialize)]
+pub struct ApplicationWithCounts {
+    pub id: i64,
+    pub name: String,
+    /// Distinct hosts that have at least one port matching this application.
+    pub host_count: i64,
+}
+
 // ─── Queries ──────────────────────────────────────────────────────────────────
 
+/// Returns all applications enriched with their associated host count.
+#[server]
+pub async fn get_applications_with_counts() -> Result<Vec<ApplicationWithCounts>, ServerFnError> {
+    use sqlx::{AnyPool, Row};
+
+    let pool = use_context::<AnyPool>()
+        .ok_or_else(|| ServerFnError::new("Database pool not found in context"))?;
+
+    let rows = sqlx::query(
+        "SELECT
+             a.id,
+             a.name,
+             COUNT(DISTINCT hp.host_id) AS host_count
+         FROM applications a
+         LEFT JOIN application_ports ap ON ap.application_id = a.id
+         LEFT JOIN host_ports hp        ON hp.port_number    = ap.port_number
+         GROUP BY a.id, a.name
+         ORDER BY a.name",
+    )
+    .fetch_all(&pool)
+    .await
+    .map_err(|e| ServerFnError::new(e.to_string()))?;
+
+    Ok(rows
+        .into_iter()
+        .map(|row| ApplicationWithCounts {
+            id:         row.get("id"),
+            name:       row.get("name"),
+            host_count: row.get("host_count"),
+        })
+        .collect())
+}
+
 /// Returns all applications ordered by name.
 #[server]
 pub async fn get_applications() -> Result<Vec<Application>, ServerFnError> {