I've never heard of doing anything other than giving it a good cleaning, as you would with any new item before first use.
I've only heard of seasoning used for cast iron and carbon steel, not for stainless steel. Looking online, I did find instructions for seasoning stainless steel, but I'd be inclined to look at the paperwork that came with the pan -- if the manufacturer recommends doing something, follow their instructions. If they don't, just give it a good wash.
This is quite common and pretty harmless. The scratches you see don't go very deep, nor are they very wide. My All-Clad saute pan is nearing 10 years old and has a ton of micro-scratches on the interior. It still performs beautifully.
That said, the scratches can grab onto proteins and cause sticking. However, this is simple to prevent with both oil and proper pan preheating.
When a pan is preheated properly the metal expands, essentially closing all of the micro-scratches. This prevents the proteins from grabbing onto them and getting stuck. You obviously need oil/fat to assist with this as well.
To properly heat a pan to the appropriate temperature I suggest using the water drop method. If you put a cold pan on heat and drip a drop of water onto it, the water will sit there for several seconds then boil away. As the pan gets warmer this will happen more quickly, fizzling away in a second or so. Once the scratches start to close something weird happens.
First, the drop of water will break into a few mini drops which scoot around the pan as they evaporate. This is a sign that you are almost there. When the drop of water stays whole (mostly) and scoots around the pan like a mercury ball, this is the perfect temperature. I the water instantly vaporizes on contact, you've gone way too far and need to let the pan cool down. At this point you should add your oil/fat, swirl it around, and immediately add your food. (Make sure the mercury ball of water is gone before adding oil).
Also note that the mercury-ball phase is definitely too hot for unclarified butter, and may be too hot for some extra-virgin olive oils. They may instantly smoke upon adding.
Again, it's important to have your oil and ingredients in place (mise en place) before you start. It's quite easy to skyrocket past the mercury-ball phase if you have to open your oil, pour, and then season your ingredients.
Best Answer
I wonder where you have read it. Your link doesn't help, maybe you linked the wrong question? It talks about using a stainless pan with oil.
If you are talking about true saute (very quick movement of bite-sized pieces of food on a very hot pan), it is completely impossible without oil. If you are misusing the term to mean shallow frying, you can do it without oil in a coated pan, if you take care not to overheat to the point of damaging the coating. Stainless steel pans have to always be used with oil or other fats, else they will stick. The taste of food browned without fat (in a coated pan) will also be different from that of food browned in fat, because fat is needed for important flavor-producing reactions. It is up to you if you like the different taste or not.
You can braise food in a broth, meaning that you put a small amount of broth in the pan, add the food and wait for it to cook through. This works with stainless steel pans too. But this is not comparable to either sauteeing or shallow frying. The temperature does not exceed 100 Celsius, which is way too low for Maillard and other flavor-developing reactions. So, if your recipe calls for sauteeing, browning, grilling or frying the food, you cannot use this method as a substitute.
In summary, you seem to have been misinformed. This is not possible, frying always requires oil, and browning without oil requires a PTFE coated pan (or a fresh ceramic coated one - they tend to lose their antistick properties with time).
Update You can sweat vegetables without oil, as mentioned in the corrected link. This is very different from both the true sauteeing you will find in textbooks and the quick browning usually meant in recipes which call to start with sauteing the ingredients. The result are softened vegetable pieces suitable for e.g. stir frying or mixing into chunky sauces. If you are going to make a soup or stew, don't bother using it instead of browning, as it doesn't add flavor and a soup doesn't mind the vegetables weeping into it. For other applications, you can try it and decide if the taste is good enough for your purposes.
The process is simple. Cut your vegetables finely (in the 4-7 mm range). Pour 3-5 mm of water into the pan and add a level layer of vegetables, up to 1.5 cm thick. Turn on the stove on slow to medium heat and leave them largely undisturbed. Wait until they are done - they will have softened and lost some moisture. As you are not using oil, you have to watch the food closely, because if all the liquid evaporates, the food will heat enough to stick and scorch. But don't stir much, because the vegetables need time in contact with the pan/broth to heat through, not to get a new side exposed to the heat each second. You could do it with constant stirring, this is the risotto method, but you will end up with preparation times similar to risotto (> 40 min) while waiting for the vegetables to heat through despite the stir. So it takes a little experience to know when the bottom of the vegetables is done but the liquid is not yet evaporated, without stirring to take a look at what is happening on the bottom.
In the end, it is up to you to decide if you really want to bother. You get a higher probability of failure (risk of scorching it), higher effort (the need to watch it closely) and less taste. If you feel that the fat reduction makes up for it, do it.