If the company that promised to sell a stock at a certain price (i.e. shorted it) goes bankrupt, who’s liable for the matched orders from the past? The market? The trading platform? If it’s the latter, how do they avoid going bankrupt themselves once shit hits the fan?

If a company shorted the stock, they not just promised to sell it, but have already sold it - by borrowing the stock from someone else. If they go bankrupt, that someone else is like any other creditor, i.e. probably will lose at least part of what they're owed