Is it permissible, in Sharia, to pardon an adulteress if she repents and shows remorse, and is inclining towards pardon considered pleasing to Allah or displeasing to Him, especially given the presence of a newborn whose lineage will be ascertained?

The pregnancy is attributed to you as long as you are the owner of the marital bed, and you cannot disavow it except through Mula'anah. As for her mistake, you should forgive her and cover for her if her remorse and uprightness become apparent, because establishing the hadd punishment is not for you. Covering up is better than raising her matter to the Imam, and Allah loves covering up and forgiveness. Encourage her to repent and embrace Islam with good treatment, for guidance is better than red camels, and Islam erases what came before it. And you must enjoin her to do good and forbid her from evil.