Is congregational prayer valid if the imam says the first salutation silently and the second aloud and does not perform the prostration of forgetfulness?

For the Imam to say the Taslim aloud is a Sunnah, not an obligation. Whoever omits saying it aloud, their prayer is valid, and no prostration of forgetfulness (sujud al-sahw) is required of them, because it is neither among the emphasized Sunnahs of prayer nor among its obligations. There is no prostration of forgetfulness for one who omits an unemphasized Sunnah.