How can I create a dropdown menu in Indesign? Like this: https://indd.adobe.com/view/f7828470-5b4b-4

You're on the right track; multi-state objects is how that is done. Just Google "indesign interactive menu" and you'll find plenty of advice on how to do it.

There is no common interactive format that allows advanced features like drop-down menus that can be hosted on a private website, other than HTML/CSS. Publish Online has many features — I don't know offhand if it has anything like drop-down or accordion menus; I don't use it myself — but the documents have to be hosted from the Adobe site. There is no option to move the documents to another host. (This dependence on Adobe's good will and sustainability of the service makes it a poor choice for anything but fairly ephemeral content and clients who don't mind the "offshore" hosting.)

If your website/web document design skills are not up to creating an interactive document, your only good solution is the InDesign plugin In5, which does export complex InDesign layouts to excellent web-based format. It's a bit pricey, though, unless you have ongoing projects for it.