Is it permissible, Islamically, to file a lawsuit seeking financial compensation from an airline company that ceased operations and did not refund the ticket prices, in order to recover only the original amount of money along with covering the exorbitant legal fees, knowing that there is no other way to recover the money except through this method?

The company is obligated to provide the contracted service or refund the price of the tickets paid. If claiming the right necessitates filing a lawsuit or appointing a lawyer, and there are financial expenses involved, then there is no blame upon you for obligating the company to bear these costs due to its procrastination and refusal to fulfill the right, in accordance with the حديث (hadith): "There should be no harm nor reciprocating harm." However, if the court rules in your favor for more than what is rightfully yours, you are not permitted to take the excess; because a judge's ruling does not make lawful what is inherently unlawful.