As someone who knows English and is learning German, the words "Handy" for smartphone, or "Beamer" for overhead projector, or "Oldtimer" for classic car all sound very out of place. Even hearing "das Baby" for a nursing-age baby (instead of the German "Säugling") sounds a bit weird.

I guess it's different when you grew up with those words and internalized them.

That's right, and I think Smartphone is actually competing with the good old word Handy, at least in the marketing department. I guess "Ich suche mein Smartphone." sounds somehow too snobbish in most casual contexts.

A handy means something entirely different in the US