What is the prison in the government district there for? Is it part of some specific NPC subquest? Is it just there for ambience?

As far as I know its only purpose is to keep produce-pushing gnomes off the streets and away from our young.

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When you meet Jan Jansen for the first time, if you admit he was selling you illegal items he is arrested and put in that prison. You can then go to the prison and pay his bail so he can join your party. That's the only use I know it has.

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Nalia is thrown in prison at some point as well. If you want to see her before you get her out, you go visit her there. Otherwise I believe it's just for Jan.

Sorry, Riftmaker, but Jan is the only recruitable NPC who goes directly to Jail without collecting $200.

The prison is (or at least can be) used if you have the Thief stronghold, but that may only be if you have the Expanded Thief Stronghold installed.

I could've sworn I saw Nalia in a prison at some point...