As in any business, the things within the business are the businesses responsibility. In other words, if you have nice things, put them away or up high. If a tail is what broke it, either move them higher or watch smaller pups. It takes time but all pet sitters learn that valuables are not good things to have below half a wall high (usually 4 ft IF you keep medium to small dogs). You can also use velcro to attach things to surfaces and such. It is definitely a learning experience.
Otherwise, the customer probably should not be asked for the replacement cost as they assume that you know better than to leave things down low or on a surface that could be bumped. If you have many really nice things, raise your price to account for cost of replacing those things if they cannot be moved. While it is really nice to have beautiful things around, in a pet sitting house, it is not pet friendly. Oh...you can also gate off a specific room for pet sitting and place the nice things in a "welcome room" where you meet the pet parents and have drop off/pick ups.
Yes - just one puppy so far and learned to seriously puppy proof and increase distractions. He even pulled curtains down! Learning as I go! Good luck!