feat(storage): support configurable install root

Add a LuCI install-root input, persist the selected path in UCI,
and route install, status, backup, uninstall, and runtime scripts
through the configured storage root for new installs.

Reference: custom install root flow

tests/test_openclaw_paths.lua

@@ -0,0 +1,37 @@
+local script_dir = arg[0]:match("^(.*)/[^/]+$")
+local repo_root = script_dir:gsub("/tests$", "")
+
+package.path = table.concat({
+	repo_root .. "/luasrc/?.lua",
+	repo_root .. "/luasrc/?/init.lua",
+	repo_root .. "/luasrc/?/?.lua",
+	package.path,
+}, ";")
+
+local paths = require("openclaw.paths")
+
+local function assert_eq(actual, expected, label)
+	if actual ~= expected then
+		error(string.format("%s: expected %q, got %q", label, expected, actual), 2)
+	end
+end
+
+local function check_root(input, expected_root, expected_base)
+	local normalized = paths.normalize_install_root(input)
+	local derived = paths.derive_paths(input)
+
+	assert_eq(normalized, expected_root, "normalized root")
+	assert_eq(derived.install_root, expected_root, "derived install root")
+	assert_eq(derived.oc_root, expected_base, "derived OpenClaw root")
+	assert_eq(derived.node_base, expected_base .. "/node", "node base")
+	assert_eq(derived.oc_global, expected_base .. "/global", "global base")
+	assert_eq(derived.oc_data, expected_base .. "/data", "data base")
+end
+
+check_root(nil, "/opt", "/opt/openclaw")
+check_root("", "/opt", "/opt/openclaw")
+check_root("/mnt/emmc/", "/mnt/emmc", "/mnt/emmc/openclaw")
+check_root("relative/path", "/opt", "/opt/openclaw")
+check_root("/", "/", "/openclaw")
+
+print("ok")

tests/test_openclaw_paths.sh

@@ -0,0 +1,30 @@
+#!/bin/sh
+set -eu
+
+SCRIPT_DIR=$(CDPATH= cd -- "$(dirname "$0")" && pwd)
+REPO_ROOT=$(CDPATH= cd -- "$SCRIPT_DIR/.." && pwd)
+
+. "$REPO_ROOT/root/usr/libexec/openclaw-paths.sh"
+
+fail() {
+	echo "FAIL: $1" >&2
+	exit 1
+}
+
+oc_load_paths "/mnt/emmc/"
+[ "$OPENCLAW_INSTALL_ROOT" = "/mnt/emmc" ] || fail "normalized install root"
+[ "$OC_ROOT" = "/mnt/emmc/openclaw" ] || fail "derived OpenClaw root"
+[ "$NODE_BASE" = "/mnt/emmc/openclaw/node" ] || fail "derived node path"
+[ "$OC_GLOBAL" = "/mnt/emmc/openclaw/global" ] || fail "derived global path"
+[ "$OC_DATA" = "/mnt/emmc/openclaw/data" ] || fail "derived data path"
+
+oc_load_paths "relative/path"
+[ "$OPENCLAW_INSTALL_ROOT" = "/opt" ] || fail "fallback install root"
+[ "$OC_ROOT" = "/opt/openclaw" ] || fail "fallback OpenClaw root"
+
+tmpdir=$(mktemp -d)
+trap 'rm -rf "$tmpdir"' EXIT INT TERM
+existing=$(oc_find_existing_path "$tmpdir/missing/nested")
+[ "$existing" = "$tmpdir" ] || fail "nearest existing path"
+
+echo "ok"