Using the Comet cleaner - suggest trying to get both sides and bottom of the sink very wet. If one has a sprayer hose at the sink, that works great.
After the sink is wet, shake the Comet all over the sink. Perhaps use water and paper towels to create a "cleaner paste" to cover the sides of the sink with the "cleaner paste.
Leaving the Comet cleaner on the walls and bottom of the sink for awhile sometimes works better - maybe at least 15 minutes.
After some time has passed, use wet paper towels to scrub the bottom and sides of the sink. Then rinse well.
(Also, as a side note, have found any "stainless steel cleaner" does not seem to work.for some. It appears to leave an oily film.)
There might be different types or grades of steel used in stainless steel sinks. So some stainless steel sinks appear more shiny than other sinks.
Hope this was helpful.