Is it permissible to eat meat from restaurants owned by "fusāq" (transgressors/sinners) if they purchase meat from suppliers known for their commitment [to Islamic dietary laws] and the correctness of the slaughter, especially given the difficulty in obtaining halal food?

The sacrifice of a transgressing Muslim is permissible, unless it is known that it was slaughtered in an unlawful manner or that it is not among the permissible sacrifices. Therefore, there is no harm in eating beef from a restaurant whose owner is a transgressor, especially if it is known that it was slaughtered in a lawful manner. And asking the restaurant owner about the reality of the meat is not excessive scrupulosity. The default ruling for the meat of wild animals is prohibition, except what the Sharia has permitted to consume, such as the sacrifice of a Muslim or a person of the Book, unlike land, whose default ruling is purity.