refactor: replace ghostty wrapper with proper CLI actions for terminfo cache management

- Add +list-ssh-cache and +clear-ssh-cache CLI actions
- Remove ghostty() wrapper functions from all shell integrations
- Improve variable naming in shell scripts for readability

Addresses @00-kat's feedback about CLI discoverability and naming
consistency. The new CLI actions follow established Ghostty patterns
and are discoverable via `ghostty --help`, while maintaining clean
separation of concerns between shell logic and cache management.

src/cli/ssh_cache.zig

@@ -0,0 +1,71 @@
+const std = @import("std");
+const Allocator = std.mem.Allocator;
+const Child = std.process.Child;
+
+/// Get the path to the shared cache script
+fn getCacheScriptPath(alloc: Allocator) ![]u8 {
+    // Use GHOSTTY_RESOURCES_DIR if available, otherwise assume relative path
+    const resources_dir = std.process.getEnvVarOwned(alloc, "GHOSTTY_RESOURCES_DIR") catch {
+        // Fallback: assume we're running from build directory
+        return try alloc.dupe(u8, "src/shell-integration/shared/ghostty-ssh-cache");
+    };
+    defer alloc.free(resources_dir);
+
+    return try std.fs.path.join(alloc, &[_][]const u8{ resources_dir, "shell-integration", "shared", "ghostty-ssh-cache" });
+}
+
+/// List cached hosts by calling the external script
+pub fn listCachedHosts(alloc: Allocator, writer: anytype) !void {
+    const script_path = try getCacheScriptPath(alloc);
+    defer alloc.free(script_path);
+
+    var child = Child.init(&[_][]const u8{ script_path, "list" }, alloc);
+    child.stdout_behavior = .Pipe;
+    child.stderr_behavior = .Pipe;
+
+    try child.spawn();
+
+    const stdout = try child.stdout.?.readToEndAlloc(alloc, std.math.maxInt(usize));
+    defer alloc.free(stdout);
+
+    const stderr = try child.stderr.?.readToEndAlloc(alloc, std.math.maxInt(usize));
+    defer alloc.free(stderr);
+
+    _ = try child.wait();
+
+    // Output the results regardless of exit code
+    try writer.writeAll(stdout);
+    if (stderr.len > 0) {
+        try writer.writeAll(stderr);
+    }
+
+    // Script handles its own success/error messaging, so we don't need to check exit code
+}
+
+/// Clear cache by calling the external script
+pub fn clearCache(alloc: Allocator, writer: anytype) !void {
+    const script_path = try getCacheScriptPath(alloc);
+    defer alloc.free(script_path);
+
+    var child = Child.init(&[_][]const u8{ script_path, "clear" }, alloc);
+    child.stdout_behavior = .Pipe;
+    child.stderr_behavior = .Pipe;
+
+    try child.spawn();
+
+    const stdout = try child.stdout.?.readToEndAlloc(alloc, std.math.maxInt(usize));
+    defer alloc.free(stdout);
+
+    const stderr = try child.stderr.?.readToEndAlloc(alloc, std.math.maxInt(usize));
+    defer alloc.free(stderr);
+
+    _ = try child.wait();
+
+    // Output the results regardless of exit code
+    try writer.writeAll(stdout);
+    if (stderr.len > 0) {
+        try writer.writeAll(stderr);
+    }
+
+    // Script handles its own success/error messaging, so we don't need to check exit code
+}