How can one prove that these planets have atmospheres by observing the coverings of stars by Venus and Mars?

When a star is covered by Venus or Mars, a gradual decrease in the brightness of the star is observed. When a star is covered by the Moon, its brightness remains constant until it disappears, unless, of course, the diffraction phenomena are taken into account.

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.