Interrupting politely is allowed, and waiting is worse.

If you let three unclear sentences go past, you now have three problems instead of one.

Confusion compounds. You miss one word, and while you are working it out you miss the next sentence, and by the time you look up the topic has moved and you cannot even name what you lost. That is how a small gap becomes a conversation you have quietly left. Stopping someone early is not an interruption in the rude sense. It is maintenance, and it protects the rest of the exchange.

The polite versions are short and everyone uses them. Sorry, can I just stop you there. Hang on, before you go on. Sorry to interrupt, can I check one thing. Say it with an upward, friendly tone and then say what you need immediately. The whole move takes three seconds and speakers barely notice it, because it is what they do to each other all day.

Watch for the natural gaps as well. There is a small pause at the end of a point, a falling tone, sometimes an audible breath. That gap belongs to whoever takes it. Learners often wait for a bigger opening that never comes, because in fast conversation there is no bigger opening. Take the small one. It is genuinely yours.