• make dataApiKeydownHandler to handle specific instance, avoiding extra manipulations
• extract createPopper method
• handle click event in one place, remove undocumented click listener on element in case of not having the proper markup
• use classList add instead of toggle on show
• simplify toggle
• remove static interface
• make isShown method

NOTE for reviewers:

Better review it, commit by commit. It will help you with the proper message and will guide you with sanity to follow the logic