The character arc of the Matchmaker in your scenario can be described as a "Catalyst" archetype. This archetype often plays a crucial role in bringing together disparate characters who may not initially see their compatibility. They act as a driving force behind significant plot developments and transformations, guiding other characters towards their destinies.
In this case, the Matchmaker overcomes objections and societal pressures to unite the bride and groom, ultimately proving that they are perfectly suited for each other. This reflects the Matchmaker's role as someone who sees the potential in others and takes action to facilitate their happiness and fulfillment, even when faced with resistance. This character's growth often involves a deeper understanding of love, relationships, and the importance of following one's instincts against conventional wisdom.