I did similar work with Hello.Vote for voter registration, and there are so many offline forms that could be improved with a bit of web/messaging UI. Also see snapfresh.org for a CfA project that helps find places that accept EBT cards.
It may be different with U.S. and Canada, though - things are a bit easier when asylum applicants are not coming over unguarded land borders.
(FWIW, I've assisted an immigrant, an old woman, in composing her complaint to the national courts and ECHR. The system is rigged against honest applicants because of the overload caused by more or less frivolous cases. We lost, too, technically, but she was in too bad shape to be deported so eventually got permission to stay.)
However, particularly for European governments, it's now becoming visible that there is a selection to be made: you can have completely open borders, or you can have a welfare state, but you can't have both.
Depressing future scenarios like this make me miss the 1980ies, when popularly feared terrible futures had clearly good solutions ("don't blow up the planet") instead of a choice between two evils.
It does not have to be like that, it is just what you believe.
Does bettering oneself mean the same thing for economic migrants as it does for Europeans, in your mind? I gather from your comment that it means "attaining greater material wealth" for economic migrants. What does it mean for Europeans? Does it mean sharing their material wealth with the less fortunate, at their expense and the expense of their progeny?
Other than chat bots, just making forms and bureaucratic processes more accessible online seems like an arena that still has vast potential for improvement.