feat: add public_answers property to questions

[Panaetius]

Some registration answers are worth sharing. Now an owner picks which.

As an owner, I want to decide question by question which answers the rest of my hackathon can read. My form asks four things: affiliation, T-shirt size, dietary needs, and whether you accept the code of conduct. Three are nobody's business but mine. The first is the most useful thing a participant could know about someone they're about to team up with — and until now only I could see it.

As a participant looking for a team, I got a list of names with a role chip, and a profile that said "Visible to organizers only." I was picking collaborators from a phone book.

Now the owner ticks "Show answers" to participants on the affiliation question and leaves the other three alone. The participant sees ETH Zurich on that profile. The T-shirt size stays where it was.

• The tick-box stays editable after people have answered — retracting a question you shouldn't have shared is exactly the thing you need to do then.
• While answering, a shared question says so under the field. That's the moment you decide what to type.
• Your own profile shows your whole form, with a Shared chip on what's public.
• Anyone else's profile shows only shared answers — the owner's view too. Their write access would fetch the whole form; not asking for it is the point.

Two bugs fixed along the way: questionEntryFromEnt never copied PublicAnswers, so the flag was writable but always read back false. And the registration form prefilled from an unfiltered answer list keyed by question — another participant's affiliation would have appeared in your form as if you'd typed it.