Strangely not including the scheme doesn't seem to consistently work on an iPhone when in uppercase, a string like "FOO.COM/BAR" does open as a URL, but a string like "FOO.UK/BAR" does a search. I think it's best to include the full HTTPS:// prefix (and I don't think it being uppercase really matters, I'd be surprised if that breaks anything).
I did a lot of trial and concluded the same: for non .COM address we had to use the full HTTPS:// prefix otherwise iOS won't open it. On Android it opens any TLDs, even unusual ones like .MD or .NZ.
