What is the ruling on studying accounting (auditing) with the intention of working in factories or institutions and avoiding working in usurious banks, and what is the Shar'i advice regarding completing this specialization?

The science of accounting is commendable and permissible to learn as long as it is not used for unlawful purposes. Therefore, if you do not intend to apply it in a prohibited field, there is no harm for you in continuing to learn it. It is advisable to consult specialists in commercial affairs to choose suitable specializations that are safe from prohibited transactions, while also emphasizing the importance of performing Istikharah.