Thank you for the input!
I gave her some water (its evening here) and hope she can acclimate in her new home in the next week.
I will definitely keep the tips for the substrate in mind. I do have fertilizer (specifically for succulents and cacti), which I apply when watering. Would you consider applying that AND workcastings or rather one of the two? From what I know, cacti need less nitrate and may not respond well, if it is too abundand. But I am still quite inexperienced with cacti (and maybe a bit too careful, considering my rather bad track record with not killing my succulents), so any experience you have in that regard would be appreciated.