While putting soil in the pot, I accidentally broken two Capanula branches with many flowers.
Is it possible to propagate using them? If yes, can anyone please guide through it?
Well its possible, but it's a performance to do it the 'official' way see link here under propagation https://gpnmag.com/article/campanula-adansa-and-ambella-series/. I think I'd just stick the end of it in a bottle of water to see if it makes roots, but you'd need to remove the flowers and any buds which have formed. When trying to root proper cuttings from a plant, its best to have shoots which are not already flowering, because the plant is already concentrating on flowering, not making roots.
The usual way with Campanula porscharkyana varieties is to dig them up and split them when the clump gets large enough, usually done in autumn or spring.