I’ve is only used when there is a verb to follow and the have is part of the verb’s construction.

As in “I’ve done it” or “I’ve seen it”

It would not be used before a noun, in the context of ownership, as in “I have a meeting”

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!

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.

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

Nah that’s just Americans. Brits and Aussies say it all the time. Not sure about Canadians.