The corporations have their own contracts with e.g. Microsoft/OpenAI. The data will likely be sent the same way as with the public tools, but the providers promise not to use it for other purposes.
how far did you go in terms of features?
I'm a hiring manager for a company in a regulated field. In addition to what has been said already, if a candidate came with a list of their own requirements for the said app, preferrably with unit tests, and/or a checklist of how much work there is still left, that would be gold.
The fact is, that probably all organisations deal with large legacy systems. If a candidate shows the capability to think a bit further than a tech demo, that's a huge plus.
I think there are many good replies already, but I feel one consideration is missing: time.
If you have the time for only one job, why wouldn't you take one paying more, even if it requires a bit more skills to achieve? You are going to do that for a long while, so living more comfortably has a value.