Migrate date picker to cally calendar-date (#29994)

* Switch date picker to cally calendar-date

* Remove app-datepicker styles from date picker dialog

Clean up unused CSS overrides in ha-dialog-date-picker.

Remove custom properties, focus/body rules, and responsive media
queries for app-datepicker and calendar-date so the component uses
upstream defaults and avoids duplicate styling

* Review

* Apply suggestion from @MindFreeze

Co-authored-by: Petar Petrov <MindFreeze@users.noreply.github.com>

* Fix date parsing in HaDialogDatePicker to handle ISO string format

* Update src/components/ha-dialog-date-picker.ts

---------

Co-authored-by: Petar Petrov <MindFreeze@users.noreply.github.com>

package.json

@@ -90,8 +90,8 @@
     "@vue/web-component-wrapper": "1.3.0",
     "@webcomponents/scoped-custom-element-registry": "0.0.10",
     "@webcomponents/webcomponentsjs": "2.8.0",
-    "app-datepicker": "5.1.1",
     "barcode-detector": "3.1.1",
+    "cally": "0.9.2",
     "color-name": "2.1.0",
     "comlink": "4.4.2",
     "core-js": "3.48.0",
@@ -221,7 +221,6 @@
     "workbox-build": "patch:workbox-build@npm%3A7.1.1#~/.yarn/patches/workbox-build-npm-7.1.1-a854f3faae.patch"
   },
   "resolutions": {
-    "@material/mwc-button@^0.25.3": "^0.27.0",
     "lit": "3.3.2",
     "lit-html": "3.3.2",
     "clean-css": "5.3.3",