I see this issue is still active. My website, running twenty twenty four theme also has the mobile menu not working.
I tried excluding the following CSS selectors from deferral and minification:
wp-block-navigation__responsive-container-open
header.wp-block-template-part
That didn’t work.
Then I disabled Perfmatters, an optimization plugin, then the menu worked. So for me, it was a plugin problem.
Still problem-solving the exact issue, but I recommend deactivating plugins to find out which is causing the issue for you.
Good luck!