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Season short ribs all over with salt and pepper. Heat oil in a pressure cooker over medium-high heat (or using the sauté or sear function on an electric multi-cooker) until shimmering. Working in batches, add short ribs and brown on all sides, about 6 minutes per side. Transfer browned short ribs to a platter and repeat with remaining short ribs.
Pour off all but 2 tablespoons of fat from the pressure cooker. Return to the heat and add celery, carrot, onion, and garlic. Cook, stirring often, until browned, about 6 minutes. Stir in tomato paste and cook for 1 minute longer; lower heat at any point if the contents threaten to burn.
Add red wine, scraping up any browned bits from bottom and sides of pot. Bring to a simmer and cook until raw alcohol smell has mostly cooked off, about 10 minutes. Add stock; if using store-bought stock, place it in a large bowl first and sprinkle all over with gelatin until bloomed, then add to pressure cooker. Make sure the liquid does not go over the pressure cooker's max fill line; if it does, use less stock.
Return short ribs to pressure cooker along with any accumulated juices, nestling them into braising liquids. Add thyme and bay leaves, then set pressure cooker to high pressure; cook for 45 minutes starting from when the cooker reaches high pressure.
Meanwhile, in a large saucepan, bring port to a very gentle simmer, regulating heat to maintain that simmer. Cook, uncovered, until reduced to a syrup-like consistency and about 1/2 cup (120ml) in volume, about 1 hour. Set aside.
Depressurize pressure cooker and remove lid (we recommend allowing it to depressurize naturally as the fat from the beef can sometimes spray through the vent when allowed to depressurize rapidly, though it is possible to do a rapid depressurization if careful). Carefully remove short ribs from pressure cooker and transfer to a clean platter (they will be very tender, so the bones may slip out; try to hold them together as you transfer them). Tent ribs with foil.
Skim accumulated fat from surface of braising liquid and discard. Strain braising liquid through a fine-mesh strainer set over a large heatproof bowl, pressing on solids to extract as much liquid as possible; discard vegetables and aromatics.
Rinse out pressure cooker, then return strained braising liquid to it. Return to heat and bring to a gentle simmer, adjusting heat to maintain simmer. Simmer, uncovered, until braising liquid is reduced to 2 cups, about 1 hour; skim any foam that accumulates on the surface as needed. Add port wine reduction to braising liquids.
The sauce should be thick enough to coat the back of a spoon and leave a trail when you drag your finger through it. If it's still a little thin, whisk in the cornstarch slurry and bring to a simmer until thickened slightly.
Season sauce with salt and pepper to taste. Return short ribs to pressure cooker, spooning the sauce all over and around them to glaze while rewarming over gentle heat. Serve.