Theoretical analysis on the possibility of superconductivity in the trilayer Ruddlesden-Popper nickelate \({\mathrm{La}}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{10}\) under pressure and its experimental examination: Comparison with \({\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}\)