Ironically (or not) I've seen smoking gun attributed to Arthur Conan Doyle in a Sherlock Holmes story. (It was smoking pistol in that story). Even if that's rubbish, I think that one is common across the English speaking world. The baseball/American football stuff is a bit different. In the commonwealth we might say "Hit for six" instead of hitting it out of the park. There are a bunch of other ones related to sports more common in England like snookered, own-goal, red card, etc.

It actually probably wouldn’t be too expensive or difficult to finetune those sayings out of default behavior if it were made accessible to you, you could even automate most of the relabeling by having the model come up with a list of idioms and appropriate replacement terms so it calls eg cookies biscuits or removes references to baseball. Absolute bollocks they don’t offer that as a simple option anymore

In my user instructions I always have a point to "always use British English" which seems to reduce Americanisms. I am yet to see Claude give me a "back of the net!" though, sadly.