It depends what you mean by interactive drop-down menu - there's two options here:
You haven't mentioned a hosting type so this is based on Cloud - although I'm pretty sure it's quite similar across Server/DC.
You can add custom templates - like the ones offered during creation such as Blank Page or Blog Post. In templates, you can have an interactive list where you choose the options before the page creates, and then the options chosen form part of the data on that page.
To be clear, the drop-down is only available here during creation - not after.
To create a template like this you'll need to be a Space Admin and then:
^ When creating a page with this template the drop-down fields will be available to choose options for during creation.
On pages themselves, having a drop-down field isn't possible natively. You could try an app - such as Easy Dropdown - or an alternative I've seen users try in the past is:
^ This isn't a drop-down list, but it's an alternative option!
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