Overheated stainless saucepan - food now sticks

Googling "Stellar non-stick stainless steel saucepan", I read that it has a coating of polytetrafluoroethylene or PTFE - Teflon being one of the brand names people are most familiar with for this product. Stellar Non-stick Cookware reads

Never use a non-stick pan on full heat - overheating it will almost certainly damage the coating. ln fact, many more nonstick pans are damaged by being overheated than by being scratched.

Sorry to say but non-stick coatings that have been over-heated are damaged and can't be salvaged.

Lifted from a similar question elsewhere on StackExchange:

If you have hard water, a soak in vinegar can be helpful. A cooked on veneer of calcium carbonate, or similar water minerals, can make food stick to the surface of the pan very tightly. Vineger will dissolve the stuff completely – Wayfaring Stranger Jul 20 '13 at 12:36

You mention you've already tried vinegar, but Wayfaring Stranger's post points up that the issue in this case is not loss of a nonstick coating, but most likely deposition of minerals from whatever was in the pan when it overheated. When I've overheated pans due to inattention (more times than I care to count), I have found that Barkeeper's Friend and aggressive, thorough scrubbing with a green Scotchbrite pad is the most reliable way to get all of the stains and deposits off. Depending on what was in the pan (proteinaceous or fatty food, for example), sometimes Bon Ami works very well, too.

From the Stellar product support page :

Excessive heat will spoil the appearance of a pan by causing tinting of the surface. Similarly, when cooking starchy foods for the first time, a bluish tinge may be imparted to the cooking surface. Neither the pan nor the food will have been harmed, and the bloom can be permanently removed by using Stellar Stainless Steel Cleaner available from your Stellar stockist.

Another bullet-point on the same page begins with:

If your purchase has a non-stick coating...

So, apparently Stellar does sell pans that are not Teflon coated.

Quality stainless steel (all-clad, calphalon, etc.) is never completely non-stick, but you can still fry an egg and have it slide right out without sticking if you follow a few best practices:

1. Your pan must be scrupulously clean.
2. Turn down the fire.
3. Cold fat to a hot pan.

By clean, I mean cleaner than clean. Dishwashers can't do it, nor can plain Dawn and a dish-sponge. A sprinkle of barkeepers friend and (when necessary) a green 3M scrungee-pad. Then dry it with a clean towel. Maybe where you live your water is pure as the Himalayan snows, but where I live, it's liquid limestone. No, you cannot air-dry it because your water residue will layer on the surface and you'll be right back where you started. If you did it right, a clean dry cotton cloth will glide over the surface like a hockey puck on wet ice.

Don't try to cook to fast. Resist the temptation to crank your burners up to high all the time. Let it take as long as it takes, turn down the heat a little, it might take a little longer, but the results will be more controlled, you'll have better food, and less likely to burn and stick. Some cooking techniques do legitimately need very high heat (like stir-fry in a wok, or searing) but they have their own rules.

Preheat your pan. It doesn't have to be NASA-hot, just hot enough to melt your butter, or shimmer your oil. Always add cold fat to a hot pan.

Here is what I would recommend based on own experience with an overheated uncoated (neither PTFE nor ceramic!) stainless steel pan: First clean the pan from burned-in remains and mineral residues using vinegar or citric acid – if it's thick and hard, bring the vinegar in the pan to boil, then let it soak for a day or two before you scrape off the burned stuff.

When the inside pan bottom is clean, put 2 table spoons of baking soda into the dry pan and use a just slightly moist, fine dense sponge to polish the inside pan bottom using firm pressure until it is as shiny as possible. Don't use the rough side of a sponge. (However, depending on the material, some dark stains may remain in the metal and never go away again.) You can also use a little bit of fine polishing liquid or cleaning liquid for ceramic stovetops, but make sure you have thoroughly cleaned off the residues of these in the pan before preparing food in it again.