Chat GPT isn't right here. The thing about these large language models is that they are giving you a statistical likelihood as to what something means, which may often be right, but won't be right in every context.
"animi causa" is an idiom that basically means 'for fun/for pleasure'. Doing something 'animi causa' is the opposite of doing it 'negotii causa' (for work), i.e. something that you do to bring you, or someone else, pleasure or joy, rather than because you are made to or someone pays you to.
Animus can mean the soul, but it can mean a whole range of things - the entry on it in Latin dictionaries is extremely long! So Chat GPT has gone for the most literal meaning, because it doesn't know Latin idiom, only the top level dictionary entries.
So literally, 'Rodulphus (presumably the Latinised version of the name, which was actually Ridolfo), whom I bore, carved this for pleasure (i.e. out of love)' as opposed to 'because he was paid to'.
Chat GPT is also wrong that GENVI is a 'variant' of genui. It is literally just a way of spelling genui! And the basic meaning of genui (past tense of gigno) is to bear, beget, produce, give birth to. It is a first person verb, with quem (whom) as its object, so Chat GPT is wrong that it would mean 'he made', it has to mean 'I made him'. There's no reason for it to speculate that the inscription has been miscarved when it makes perfectly good sense.