How to clean stainless steel pans without scratching?

White vinegar and water 50/50 and a microfiber cloth

Go to your Dollar Store and purchase AWESOME it works.

Simple Green works well for that .

Stainless steel liquid cleaner or Barkeeper Friend

Mr Clean magic eraser.

Baking soda is my go to kitchen appliance scrub.

Spray with oven cleaner, place pan in plastic bag per instructions to allow cleaner to work without drying out. Rinse and scrub with non-scratching scrubber. For stubborn remains I would feel comfortable using a very fine (#0000) steel wool, not kitchen steel wool products, to polish away stains.

Brillo pads. I keep a used one in the freezer so it won't rust. Btw, I have a pan just like yours. The pad won't scratch it.

Use a microfiber cloth and barkeepers friend

Bar Keeper's Friend, either the powder or the liquid, and a gentle scrubby should help get a bunch of gunk off.

Make a paste with baking soda and water and spread it onto the pan, best done in the sink. Let this set overnight and then in the morning scrub with the coarser side of a scrubbie sponge from the dollar store. Repeat as needed.

• Use the Right Tools - Always use a non-abrasive or “stainless steel approved scrubber”. Stay away from mechanically abrasive scrubbers like steel wool or wire scrubbers. When stainless steel is scratched, it becomes vulnerable to corrosion.
• Scrub with the Grain - Stainless steel has polish lines that look similar to grain lines. Always scrub parallel with the polish lines.
• Avoid Chlorides - Exposure to chlorides over time can result in stainless steel becoming pitted, which makes the surface vulnerable to rust and corrosion. Chlorides are present in salt, hard water, and chlorinated cleaners.