Mobile repair shop broke my phone, would they legally have to sort the issue out?

So I took my iPhone 11 Pro to a reputable mobile repair shop near me to get the battery replaced and after I came back the chaps at the shop told me they broke the cable that is responsible for the volume and silent switch and I needed to come back on Monday so the boss could have a look at it. Hopefully they can get it sorted but I’m worried in case they don’t because it was working perfectly beforehand- if they can’t or won’t fix it would they have to compensate me for the damage? Thanks