Is repeating the phrase "no human is perfect" while recalling that the Messenger of Allah, peace and blessings be upon him, is included in it, considered apostasy that affects the marriage contract, or is it merely a groundless whisper to be ignored?

This is all from whispers (waswasah), and one must ignore it and seek refuge in Allah from Satan. Absolute perfection belongs to Allah alone, and the perfection of the Prophet Muhammad, peace be upon him, is the perfection of humanity. What you have mentioned does not affect the infallibility of marriage or the bond of Islam, and one must beware of Satan's manipulation and whispers.