How can a coda extend or strengthen the ending of a sonata-form movement?

In sonata form, a coda serves as a concluding section that extends or strengthens the movement by providing a final resolution to musical conflicts that may remain even after the recapitulation.12

A coda can enhance a movement in several ways:

• Thematic Re-elaboration: It often features extensions or creative reworkings of thematic material previously introduced, allowing for a final synthesis of the movement's ideas.1
• Tonal Balance: Composers frequently use the coda to introduce subdominant harmony, which acts as a tonal counterbalance to the tonic-dominant relationship established during the exposition.1
• Structural Expansion: While some codas are brief, others are of significant length. In some cases, such as in Beethoven’s Piano Sonata No. 23 (Appassionata), the coda is so extensive that it functions almost like a second development section, providing a dramatic climax or a triumphant transformation of the main theme.12
• Complex Texture: It can serve as a space for complex musical techniques, such as the fugal combination of multiple motives, as seen in the finale of Mozart’s Symphony No. 41 (Jupiter).1