I learned that match maker uses mmr to calculate how many sr should I gain or lose after each game ends.
But I wonder if the match maker uses mmr to find opponents who are not exactly at my sr range but at my mmr range. Because mmr can be much higher or lower than sr.
Any answer would be much appreciated.
MMR is close to SR, except for diamond+ players who have decayed. See How Competitive Skill Rating Works (Season 11) for a more complete explainer, especially the first few sections.
Match Making Rating is an elaborate handicapping system. Blizzard keeps it hidden from users because they want us to ignore it.