Is it permissible to pay the fidya for feeding the poor — which is for not fasting Ramadan due to health reasons — to an orphan sponsorship project, knowing that this money will be spent on the orphan’s food and other expenses?

Whoever breaks their fast in Ramadan due to illness must make up the days they missed. If their illness is incurable, then they must feed a poor person for each day. It is permissible to give the expiation to poor orphans, provided that it is specifically used for feeding them only, and not for other purposes.