Hello, @homme143,
Sound’s Good!! that your previous issues were solved.
And for the Vendor Button place issue, Unfortunately, this is not possible to place it in the Menu Items as the Menu is in a different div and also the button is in a different div: https://postimg.cc/rzj96FHR
And I have tested this by activating the default WordPress Theme Twenty Twenty-Two on your site as well and the result is the same: https://postimg.cc/t74xxdr7
So it makes clear that the issue is not because of our theme but it is the default styling of the plugin, if you want to change it, then it requires extra Customization.
Regards 8Themes Team.