[darrenf]

Wait, what? Englishman in my 50s here and I use phrases like that all the time — “I’ll be missing standup cos I’ve a GP appointment”, “leaving at lunchtime as I’ve a train to catch”, “gotta dash, I’ve chores to do”. No one’s ever said I sound German!

[mpyne]

I think it's more fair to call it a distinguisher of American English vs. British English.

Even just reading "I've a train to catch" gives a British accent in my mind.

[timc3]

A particular part of Britain as well. I have never used “I’ve” in that way ( I speak more RP than with an accent)