In the film universe, X-23 does NOT have a full adamantium-coated skeleton like Logan does (which is also the case in the comics). Instead, her organic bone claws were surgically removed, coated with adamantium, then re-inserted. One of the promotional videos for the film takes the form of a "leaked" video that shows what's being done to her by the project, and several scenes show the claws being surgically inserted:
If you look just below her feet in that screenshot, you can see four of the six claws still laying on the table. They're already coated with adamantium at this point, so they're going back in. Since there is blood on her feet & legs and only four claws left, they presumably already put in the two foot claws and are now preparing the arms.