The browser
For a page Downbit can't read from its link, open it in Downbit's browser and play the video. What the page plays shows up beside it, ready to download.
Any page
Choose File → Open Browser (⌘B), go to the page and play its video. Media on This Page, on the right, lists each stream and file it plays, with its qualities: download one, or Download All.
Download Page in the toolbar downloads the page itself, as a link pasted in the field would, but signed in as you are in the browser.
Signing in
Sites you sign in to in Downbit's browser stay signed in for every download. Sign in to Instagram or Facebook there to download private posts, or to a site's membership for members-only videos; signed in to Bilibili, its videos come in 1080p and more.
Settings → Browser → Sign out everywhere forgets every sign-in, with the browser's history and cache.