Add a test that checks if the mobile menu is closed by default

[essenmitsosse]

We need to add a check that the menu is closed by default and opens on request. Also, we need to check logic isolation and reusability (related - #1481)

[howwohmm]

Hey — I'll take this. Adding tests that verify the mobile menu is closed by default, opens on request, and emits close events on backdrop/button click. PR incoming.